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 16'
2018: Gazinsky 12'
2014: Marcelo (own goal) 11'
2010: Tshabalala 55'
2006: Lahm 6'
2002: Diop 30'
1998: César Sampaio 5' (or 4' according to some sources)
1994: Klinsmann 61'
1990: Omam-Biyik 67'
1986: Altobelli 43'
1982: Vandenbergh 62'
1978: Rossi 29'1
1974: Breitner 18'1
1970: Dermendzhiev 13' 1
1966: Pelé 15', Held 15' 1
1962: Facundo 4'3
1958: Simonsson 17'
1954: Milutinovic 15'3
1950: Ademir 30'
1938: Gauchel 29'
1934: Belis 4'3
1930: Laurent 19'3
1The first match of the tournament was a goalless draw, this goal is not from the opening match.
2The first two matches of the tournament were goalless draws.
3 Several matches started at the same time (so there was really no opening match of the tournament).
Sources:
general: Wikipedia article List of FIFA World Cup opening matches, 1, 2, 3
2022 Wikipedia - 2022 FIFA World Cup, Statistics, Group stage, Group A
2018 Wikipedia - 2018 FIFA World Cup, Statistics, Group stage, Group A
2014 Wikipedia - 2014 FIFA World Cup, Results, Group A, 1, 2
2010 Wikipedia - 2010 FIFA World Cup, Statistics, Results, Group A, 1, 2
2006 Wikipedia - 2006 FIFA World Cup, Group A, Results, 1, 2, 3, 4
2002 Wikipedia - 2002 FIFA World Cup, Statistics, Results, Group A, 1, 2
1998 Wikipedia - 1998 FIFA World Cup, Results, Group A, 1, 2/2a (this source says it was scored at 3:48), 3/3a
1994 Wikipedia - 1994 FIFA World Cup, Results, Group C, 1
1990 Wikipedia - 1990 FIFA World Cup, Results, Statistics, Group B, 1, 2
1986 Wikipedia - 1986 FIFA World Cup, Results, Group A, 1
1982 Wikipedia - 1982 FIFA World Cup, Results, Group 3, 1
1978 Wikipedia - 1978 FIFA World Cup, Group stage, Group 1, 1
1974 Wikipedia - 1974 FIFA World Cup, Group stage, 1
1970 Wikipedia - 1970 FIFA World Cup, Results, Group 4, 1
1966 Wikipedia - 1966 FIFA World Cup, Group stage, 1, 2
1962 Wikipedia - 1962 FIFA World Cup, Group stage, 1
1958 Wikipedia - 1958 FIFA World Cup, Group stage, 1
1954 Wikipedia - 1954 FIFA World Cup, Group stage, 1
1950 Wikipedia - 1950 FIFA World Cup, Group stage, 1
1938 Wikipedia - 1938 FIFA World Cup, Final tournament, 1
1934 Wikipedia - 1934 FIFA World Cup, Final tournament, 1
1930 Wikipedia - 1930 FIFA World Cup, Group stage, Group 1, 1, 2