Here is an answer listing times of first goals in FIFA World Cups. It is community wiki, feel free to edit it - correct mistakes, add more sources, etc.

2022: [Valencia](https://en.wikipedia.org/wiki/Enner_Valencia) 16'<br>
2018: [Gazinsky](https://en.wikipedia.org/wiki/Yury_Gazinsky) 12'<br>
2014: [Marcelo](https://en.wikipedia.org/wiki/Marcelo_(footballer,_born_1988)) (own goal) 11'<br>
2010: [Tshabalala](https://en.wikipedia.org/wiki/Siphiwe_Tshabalala) 55'<br>
2006: [Lahm](https://en.wikipedia.org/wiki/Philipp_Lahm) 6'<br>
2002: [Diop](https://en.wikipedia.org/wiki/Papa_Bouba_Diop) 30' <br>
1998: [César Sampaio](https://en.wikipedia.org/wiki/C%C3%A9sar_Sampaio) 5' (or 4' according to some sources)<br>
1994: [Klinsmann](https://en.wikipedia.org/wiki/J%C3%BCrgen_Klinsmann) 61'<br>
1990: [Omam-Biyik](https://en.wikipedia.org/wiki/Fran%C3%A7ois_Omam-Biyik) 67'<br>
1986: [Altobelli](https://en.wikipedia.org/wiki/Alessandro_Altobelli) 43'<br>
1982: [Vandenbergh](https://en.wikipedia.org/wiki/Erwin_Vandenbergh) 62'<br>
1978: [Rossi](https://en.wikipedia.org/wiki/Paolo_Rossi) 29'<sup>1</sup><br>
1974: [Breitner](https://en.wikipedia.org/wiki/Paul_Breitner) 18'<sup>1</sup><br>
1970: [Dermendzhiev](https://en.wikipedia.org/wiki/Dinko_Dermendzhiev) 13' <sup>1</sup><br>
1966: [Pelé](https://en.wikipedia.org/wiki/Pel%C3%A9) 15', [Held](https://en.wikipedia.org/wiki/Sigfried_Held) 15' <sup>1</sup><br>
1962: [Facundo](https://en.wikipedia.org/wiki/H%C3%A9ctor_Facundo) 4'<sup>3</sup><br>
1958: [Simonsson](https://en.wikipedia.org/wiki/Agne_Simonsson) 17'<br>
1954: [Milutinovic](https://en.wikipedia.org/wiki/Milo%C5%A1_Milutinovi%C4%87) 15'<sup>3</sup><br>
1950: [Ademir](https://en.wikipedia.org/wiki/Ademir_Marques_de_Menezes) 30'<br>
1938: [Gauchel](https://en.wikipedia.org/wiki/Josef_Gauchel) 29'<br>
1934: [Belis](https://en.wikipedia.org/wiki/Ernesto_Belis) 4'<sup>3</sup><br>
1930: [Laurent](https://en.wikipedia.org/wiki/Lucien_Laurent) 19'<sup>3</sup><br>

<sup>1</sup>The first match of the tournament was a goalless draw, this goal is not from the opening match.  
<sup>2</sup>The first two matches of the tournament were goalless draws.  
<sup>3</sup> Several matches started at the same time (so there was really no opening match of the tournament).

<hr>

**Sources:**

general: Wikipedia article [List of FIFA World Cup opening matches](https://en.wikipedia.org/wiki/List_of_FIFA_World_Cup_opening_matches), [1](https://books.google.com/books?id=OkSTxbAwc3YC), [2](https://books.google.sk/books?id=FdpMrBfmEJQC), [3](https://books.google.sk/books?id=4uJdBgAAQBAJ)<br>
2022 Wikipedia - [2022 FIFA World Cup](https://en.wikipedia.org/wiki/2022_FIFA_World_Cup), [Statistics](https://en.wikipedia.org/wiki/2022_FIFA_World_Cup_statistics), [Group stage](https://en.wikipedia.org/wiki/2022_FIFA_World_Cup#Group_stage), [Group A](https://en.wikipedia.org/wiki/2022_FIFA_World_Cup_Group_A)<br>2018 Wikipedia - [2018 FIFA World Cup](https://en.wikipedia.org/wiki/2018_FIFA_World_Cup), [Statistics](https://en.wikipedia.org/wiki/2018_FIFA_World_Cup_statistics), [Group stage](https://en.wikipedia.org/wiki/2018_FIFA_World_Cup#Group_stage), [Group A](https://en.wikipedia.org/wiki/2018_FIFA_World_Cup_Group_A)<br>
2014 Wikipedia - [2014 FIFA World Cup](https://en.wikipedia.org/wiki/2014_FIFA_World_Cup), [Results](https://en.wikipedia.org/wiki/2014_FIFA_World_Cup#Results), [Group A](https://en.wikipedia.org/wiki/2014_FIFA_World_Cup_group_stage#Group_A), [1](https://www.fifa.com/tournaments/mens/worldcup/2014brazil/match-center/300186456), [2](http://www.reuters.com/article/us-soccer-world-m1-bra-cro-owngoal-idUSKBN0EN2E520140613)<br>
2010 Wikipedia - [2010 FIFA World Cup](https://en.wikipedia.org/wiki/2010_FIFA_World_Cup), [Statistics](https://en.wikipedia.org/wiki/2010_FIFA_World_Cup_statistics), [Results](https://en.wikipedia.org/wiki/2010_FIFA_World_Cup#Results), [Group A](https://en.wikipedia.org/wiki/2010_FIFA_World_Cup_Group_A), [1](https://www.fifa.com/tournaments/mens/worldcup/2010south-africa/match-center/300061454), [2](http://www.uefa.com/news/newsid=1497143.html)<br>
2006 Wikipedia - [2006 FIFA World Cup](https://en.wikipedia.org/wiki/2006_FIFA_World_Cup), [Group A](https://en.wikipedia.org/wiki/2006_FIFA_World_Cup_Group_A), [Results](https://en.wikipedia.org/wiki/2006_FIFA_World_Cup#Results), [1](https://www.fifa.com/tournaments/mens/worldcup/2006germany/match-center/97410001), [2](https://www.theguardian.com/football/2006/jun/17/worldcup2006.sport2), [3](http://www.uefa.com/teamsandplayers/players/player=63033/profile/), [4](https://books.google.com/books?id=FdpMrBfmEJQC&pg=PA506)<br>
2002 Wikipedia - [2002 FIFA World Cup](https://en.wikipedia.org/wiki/2002_FIFA_World_Cup), [Statistics](https://en.wikipedia.org/wiki/2002_FIFA_World_Cup_statistics), [Results](https://en.wikipedia.org/wiki/2002_FIFA_World_Cup#Results), [Group A](https://en.wikipedia.org/wiki/2002_FIFA_World_Cup_Group_A), [1](http://www.fifa.com/worldcup/matches/round=43950100/match=43950001/index.html#nosticky), [2](http://www.dailymail.co.uk/sport/worldcup2014/article-2656049/World-Cup-opening-matches-From-Brazils-win-against-Scotland-Siphiwe-Tshabalala-screamer-versus-Mexico.html)<br>
1998 Wikipedia - [1998 FIFA World Cup](https://en.wikipedia.org/wiki/1998_FIFA_World_Cup), [Results](https://en.wikipedia.org/wiki/1998_FIFA_World_Cup#Results), [Group A](https://en.wikipedia.org/wiki/1998_FIFA_World_Cup_Group_A), [1](https://www.fifa.com/tournaments/mens/worldcup/1998france/match-center/4000), [2](http://www.fifa.com/worldcup/news/y=1998/m=6/news=fastest-goal-award-cesar-sampaio-still-unbeaten-71690.html)/[2a](http://web.archive.org/web/20170123202519/https://www.fifa.com/worldcup/news/y=1998/m=6/news=fastest-goal-award-cesar-sampaio-still-unbeaten-71690.html) (this source says it was scored at 3:48), [3](http://www.fifa.com/worldcup/videos/y=2014/m=6/video=1998-fifa-world-cuptm-sampaio-s-goal-against-scotland-2363457.html)/[3a](https://web.archive.org/web/20161101110706/http://www.fifa.com/worldcup/videos/y=2014/m=6/video=1998-fifa-world-cuptm-sampaio-s-goal-against-scotland-2363457.html)<br>
1994 Wikipedia - [1994 FIFA World Cup](https://en.wikipedia.org/wiki/1994_FIFA_World_Cup), [Results](https://en.wikipedia.org/wiki/1994_FIFA_World_Cup#Results), [Group C](https://en.wikipedia.org/wiki/1994_FIFA_World_Cup_Group_C), [1](https://www.fifa.com/tournaments/mens/worldcup/1994usa/match-center/3049)<br>
1990 Wikipedia - [1990 FIFA World Cup](https://en.wikipedia.org/wiki/1990_FIFA_World_Cup), [Results](https://en.wikipedia.org/wiki/1990_FIFA_World_Cup#Results), [Statistics](https://en.wikipedia.org/wiki/1990_FIFA_World_Cup#Statistics), [Group B](https://en.wikipedia.org/wiki/1990_FIFA_World_Cup_Group_B), [1](https://www.fifa.com/tournaments/mens/worldcup/1990italy/match-center/26), [2](http://www.the42.ie/cult-world-cup-teams-cameroon-1990-2115922-Jun2014/)<br>
1986 Wikipedia - [1986 FIFA World Cup](https://en.wikipedia.org/wiki/1986_FIFA_World_Cup), [Results](https://en.wikipedia.org/wiki/1986_FIFA_World_Cup#Results), [Group A](https://en.wikipedia.org/wiki/1986_FIFA_World_Cup_Group_A), [1](https://www.fifa.com/tournaments/mens/worldcup/1986mexico/match-center/459)<br>
1982 Wikipedia - [1982 FIFA World Cup](https://en.wikipedia.org/wiki/1982_FIFA_World_Cup), [Results](https://en.wikipedia.org/wiki/1982_FIFA_World_Cup#Results), [Group 3](https://en.wikipedia.org/wiki/1982_FIFA_World_Cup_Group_3), [1](https://www.fifa.com/tournaments/mens/worldcup/1982spain/match-center/749)<br>
1978 Wikipedia - [1978 FIFA World Cup](https://en.wikipedia.org/wiki/1978_FIFA_World_Cup), [Group stage](https://en.wikipedia.org/wiki/1978_FIFA_World_Cup#Group_stage), [Group 1](https://en.wikipedia.org/wiki/1978_FIFA_World_Cup_Group_1), [1](https://www.fifa.com/tournaments/mens/worldcup/1978argentina/match-center/2347)<br>
1974 Wikipedia - [1974 FIFA World Cup](https://en.wikipedia.org/wiki/1974_FIFA_World_Cup), [Group 1](https://en.wikipedia.org/wiki/1974_FIFA_World_Cup_Group_1), [1](https://www.fifa.com/tournaments/mens/worldcup/1974germany/match-center/2003)<br>
1970 Wikipedia - [1970 FIFA World Cup](https://en.wikipedia.org/wiki/1970_FIFA_World_Cup), [Results](https://en.wikipedia.org/wiki/1970_FIFA_World_Cup#Results), [Group 4](https://en.wikipedia.org/wiki/1970_FIFA_World_Cup_Group_4), [1](https://www.fifa.com/tournaments/mens/worldcup/1970mexico/match-center/1780)<br>
1966 Wikipedia - [1966 FIFA World Cup](https://en.wikipedia.org/wiki/1966_FIFA_World_Cup), [Group stage](https://en.wikipedia.org/wiki/1966_FIFA_World_Cup#Group_stage), [1](http://www.fifa.com/worldcup/matches/round=238/match=1656/index.html#nosticky), [2](http://www.fifa.com/worldcup/matches/round=238/match=1596/index.html#nosticky)<br>
1962 Wikipedia - [1962 FIFA World Cup](https://en.wikipedia.org/wiki/1962_FIFA_World_Cup), [Group stage](https://en.wikipedia.org/wiki/1962_FIFA_World_Cup#Group_stage), [1](http://www.fifa.com/worldcup/archive/chile1962/matches/index.html)<br>
1958 Wikipedia - [1958 FIFA World Cup](https://en.wikipedia.org/wiki/1958_FIFA_World_Cup), [Group stage](https://en.wikipedia.org/wiki/1958_FIFA_World_Cup#Group_stage), [1](http://www.fifa.com/worldcup/matches/round=220/match=1415/index.html#nosticky)<br>
1954 Wikipedia - [1954 FIFA World Cup](https://en.wikipedia.org/wiki/1954_FIFA_World_Cup), [Group stage](https://en.wikipedia.org/wiki/1954_FIFA_World_Cup#Group_stage), [1](http://www.fifa.com/worldcup/matches/round=211/match=1276/index.html#nosticky)<br>
1950 Wikipedia - [1950 FIFA World Cup](https://en.wikipedia.org/wiki/1950_FIFA_World_Cup), [Group stage](https://en.wikipedia.org/wiki/1950_FIFA_World_Cup#Group_stage), [1](http://www.fifa.com/worldcup/matches/round=208/match=1187/index.html#nosticky)<br>
1938 Wikipedia - [1938 FIFA World Cup](https://en.wikipedia.org/wiki/1938_FIFA_World_Cup), [Final tournament](https://en.wikipedia.org/wiki/1938_FIFA_World_Cup#Final_tournament), [1](http://www.fifa.com/worldcup/matches/round=206/match=1165/index.html#nosticky)<br>
1934 Wikipedia - [1934 FIFA World Cup](https://en.wikipedia.org/wiki/1934_FIFA_World_Cup), [Final tournament](https://en.wikipedia.org/wiki/1934_FIFA_World_Cup#Final_tournament), [1](http://www.fifa.com/worldcup/matches/round=204/match=1102/index.html#nosticky)<br>
1930 Wikipedia - [1930 FIFA World Cup](https://en.wikipedia.org/wiki/1930_FIFA_World_Cup), [Group stage](https://en.wikipedia.org/wiki/1930_FIFA_World_Cup#Group_stage), [Group 1](https://en.wikipedia.org/wiki/1930_FIFA_World_Cup_Group_1), [1](http://www.fifa.com/worldcup/matches/round=201/match=1096/index.html#nosticky), [2](http://www.fifa.com/worldcup/news/y=2010/m=6/news=raiders-the-first-goal-1233723.html)