Is it possible to get 100% accuracy in a game?
If you play e4 and then for some reason the opponent resigns, then yes. But there are loads of ways to do it other than stuff like resigning defo.

My opponent had 100% in this game: https://www.chess.com/analysis/game/live/137022682952?tab=review&move=8

Yes it's possible, somehow I got a perfect game. Though it was against a low ranked player. But I lost a lot trying to get a perfect score so don't mind my rank in the screenshot. The screenshot link might not work.
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I got 99.6% accuracy, but my moves were all book moves or perfect moves. Is it possible to get 100% accuracy?
https://www.chess.com/analysis/game/live/4374335351?tab=report
Chess is not a 'solved' game.
There's a theory that if both players play perfectly then the game will end in a draw.
But that's never been proven.
Because 'perfectly' (from the opening position) isn't known yet.
Number of possible chess positions is a 45 digit number so today's computers can't solve chess.
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What about just one of the players playing perfectly?
Not known for move 1.
But after f3 e5 g4 ... then Qh4# for checkmate looks perfect enough.
But that's on move 2. Not move 1.
This is a very quick game, but it's a 100% game.