Losing a game without committing any mistake

e4,e5, White resigns.

I don't know if there is such a game in the database, but why should it be theoretically impossible? You shouldn't regard engine evaluations for anyhow close to truth.

The prevailing hypothesis is that chess is a draw with best play from both sides. So every lost game must contain at least one mistake by the losing side. Sometimes the mistake is hard to find, but it must be there. Examples are engine against engine games from the TCEC championship. Most end in draws, but the decided games contain at least one mistake which was misjudged by the losing engine and taking advantage of by the winning engine.

If you play an opening that gives the other side a long term strategic advantage, then you can lose without mistakes. Or one could say the mistake is playing that opening in the first place. Take a look at some of Alphazero vs Stockfish games where Alphazero was able to gain space and limit the mobility of Stockfish's light-squared bishop. Stockfish thought it was better until later realized that it was indeed losing. You can't point out to any particular mistakes.