This link explores a way that white can force a draw. Perhaps this is game-breaking and makes the solution process much easier.
I am only an casual chess player and I’m mainly transcribing “5D Lexi”’s analysis.
My attempt at transcribing it (there’s no standard notation for 5D chess)
- e3 Kf6
- Bb5 c6
- c3 ...
The idea is for white to go for Qb3 and then Queen to f7 to move 1. Black should not play cxb5 because he needs active counter play against this idea.
- ... Qc7
- Qb3 d5 (defending this timeline)
- Qf7 to turn 1 (check) Kxf7 (the following is all in this new timeline)
- Kf3 Kf6
- Ke5 one move back in the same timeline (critical move)
Note: the new timeline is an inactive timeline, so Black doesn’t have to play here. This might be the reason that it’s a forced draw, not a win.
Now, black has difficulties creating another timeline without losing. Because if Black time-travels to a location after move 2, then the present is shifted to move 2, but white’s Knight is checkmating Black’s King on the adjacent timeline.
Black can conceivably travel further back, to turn 1, to defend.
Honestly just watch the video :)