Has this type of situation been mathematically solved? Is there a solved endgame somewhere that probably describes this to a certain degree of statistical precision?
So we have Stockfish with 8 pawns + king on one side, versus GM with all the pieces on the other?
You wonder if there is any chance of Stockfish winning that game?
Sorry to disappoint you, but the answer is resounding no.
Human has 7 extra pieces -> 2 bishops + 2 knights + 2 rooks + a queen.
The easiest way for a human to win is to trade all of their pieces for computer's pawns -> one piece sacrifices itself for one pawn.
Since we have 7 pieces, and computer has 8 pawns, after human sacrifices each piece for an opposing pawn, computer is left with a single pawn while human player has 8 pawns left.
At this point, human will just start rolling pawns to exchange the last remaining pawn. At that point human has 7 pawns + a king versus computer's lone king, which even a child can win effortlessly.
Below is a small example game I played vs Stockfish:
[FEN "4k3/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQ - 0 1"] 1. e4 e6 2. Bc4 Ke7 3. Bxe6 fxe6 4. Qg4 Kf7 5. Qxe6+ Kxe6 6. d4 Ke7 7. Bf4 Kd8 8. Bxc7+ Kxc7 9. Nc3 Kc8 10. Nb5 Kb8 11. Nxa7 Kxa7 12. Nf3 g6 13. Ne5 d6 14. Nxg6 hxg6 15. O-O-O Kb6 16. Rd3 Kc6 17. Rb3 b6 18. Rxb6+ Kxb6 19. h4 Kc6 20. Rh3 Kd7 21. Rg3 Ke6 22. Kd2 Kf6 23. Rxg6+ Kxg6 24. e5 d5 25. c4 dxc4 26. Kc3 Kh5 27. g3 Kg4 28. Kxc4 Kf5 29. a4
Human player can win this in so many ways, but I have just mentioned a "no brainer" to illustrate just how hopeless is computer's position.
After your question I was wondering if I can win stockfish in full power by having two more rooks and a knight and a bishop in the starting position. It took me about 50 moves but it was not hard at all. You can try it yourself, just trade the pieces away. I think masters can win stockfish just by having two extra pawns or a piece more compared to the stockfish.
The old time.of handycap chess is over except against weak players. Carlsen would lose 99% of his games with a knight handycap against a decent IM in serious games. In rapids or.in blitz, he'd win a bit more but would still have a hard time. And the same applies if Stockfish starts down a knight against Carlsen in long games, he'd win 1% or so, on rare blunders, and only if specidfifically reprogrammed to try to reach complex situations, avoiding too symetric openings.