Yes, it is indeed possible to get a 100% accuracy game albeit rather unlikely.
I got 100 percent accuracy!!! ( Is it possible to get 100 percent accuracy??)

https://www.chess.com/analysis/game/live/127761687767?tab=review
I got 100% accuracy in an 8 move game + I got checkmate
This is a 1 move short game that i won when i reviewed it. I saw me and my opponent had got 100 percent accuracy and yes it is possible. Here is the game:
I played the Scandinavian Defence and my opponent resigned.