As is well known, neither the 0-ply game, the starting state, nor 1-ply games, all of white's first moves, have rigorously proven outcomes. Not even first moves for white considered very bad (1. g4) can be rigorously shown to be a draw or a win for black given perfect play.
On the other hand, there trivially (1. f3 e6 2. g4) exist boards reachable in 3 plies which have proven outcomes.
But: Is it feasible to push this one ply lower? That is, can it currently be shown that there exists at least one combination of first moves by white and black resulting in a state where the result of perfect play is known?
My gut feeling would be that lowering from 3 to 2 plies changes the problem from trivial to impossible within current physical constraints of computers, but I would be very happy to hear if one of the 400 2-ply possibilities can be theorized to be within grasp.