This article (archive link) about the Scottish team Berwick Rangers centenary refers to the first competitive game:
The fishermen of the Greens also formed a football club around the same time, called the 'Royal Oaks.' They shared the field with Berwick Rangers. The first ever competitive football match in Berwick was a local derby between these teams on February 16, 1884. The result was 'a win for the Rangers by one goal and "two tries" to nil.' - proving that the rules of this new game were still not very clear.
I'm aware that the initial rules were not clear back then, but I wonder if there is any record of what a "try" could have been or why it was recorded as a score.