The Fisher 960 variant tries to do this, but it can be very different from regular chess, and some of the positions are unbalanced.
I think we can use the fact that engines know when a position is even. There must be millions of even positions in the first 10 or so moves. Pick one of those randomly, and start the game.
To make top level chess more interesting I have a handful of ideas that work in tandem.
1. Change the scoring and rating systems so that a win is worth more than two draws. E.g a win is 3 points for the winner, draw is 1 point to each player. Game theoretically this should favour players that play for a win and avoid easy draws. But also modifying the rating system is crucial, otherwise we'll get the same drawmeisters dominating the rating list.
2. Change the repetition rule to be similar to xiangqi(Chinese chess) where repetitions are illegal and don't lead to a draw. This eliminates most of the lowest effort draws right out of the gate.
3. Make the game sharper and more complex. The easiest way to do this is just to remove the concept of castling altogether. Former world champion Kramnik has advocated this, and computer analyses of the ruleset is promising. King safety is suddenly a hard problem to solve in most openings and the game becomes much, much sharper.
4(optional). add more pieces. The best way is Seirawan-chess, a modification of Capablanca chess that adds a knight-bishop(hawk) and knight-rook(elephant) without changing the board geometry and starting position.
Norway chess also has the spectaculary stupid idea that if a game is drawn, the players play an armageddon(white gets more time, black wins with a draw) blitz game, and the winner gets half a point extra, so 1.5 to 1. This just ruins it to me. A draw should still be a draw, sometimes the players were just equal and not all draws are lazy. And this makes drawing more attractive again because if you win the armageddon you still get half a victory worth of points. And decided by a blitz game in a classical tournament.
Bishop, Rook, Knight, King, Knight, Rook, Queen, Bishop. Here's the post: https://www.reddit.com/r/chess/comments/yeregq/fischer_rando...
Maybe this should be used as the starting point? Traditional openings would usually give an advantage to White.
One way to adjust would be to have everyone in a round play the same position, and calibrate. As in if black wins 90% of the games, a white win counts for more.