The first move is actually easy to spot- as the position stands, the pawns are locked place, the kings are facing off across 6 empty uncontrolled squares- white just takes the long distance oppisition across 5 squares- equally effective as across 1 or 3 squares. Black will do best to try to induce an error by keeping to the 8th rank, but white just follows keeping the opposition at first, as long as all the squares between the kings are available to the white king:

1.Kg2! Kf8 2.Kf2! Ke8!?

The most critical juncture. the natural instinct here is to keep the long distance opposition with 3.Ke2, but that would lead to a forced draw- the white king can't occupy e4- just to illustrate:

3.Ke2? Ke7! 4.Ke3 Ke6! and black now has the true oppostion since white can't play 5.Ke4 here. I will leave the rest of the puzzle to others to figure out how to proceed on move 3 for white here.