We have no way of knowing this, chess isn't remotely close to being solved. We only know that as opening theory digs deeper, it finds it harder and harder to find advantages for white, so the game is probably a draw. But that's no proof.
If the game is a draw, then any game that is won by either side must involve at least 1 wrong move. But we don't know which move was wrong. It is likely that most games involve quite a few bad moves. Mine do, anyway.
Using a computer doesn't help -- they're nowhere near strong enough. A match between the two strongest computers on really strong hardware gives many decisive results, so they're not playing perfectly, and they look much deeper than 10 ply. Their scores (+2, -2, etc) are merely estimates and not the final truth.
White does have a practical advantage, proven by the fact that white consistently scores a little bit better than black on all levels. Apparently, white gets positions that are easier to play right.