Strategy-stealing in chess 
Is it proved that white can guarantee at least draw in chess?

A while ago I was told that it was proved using strategy-stealing, but I cannot find a reference.
Postscript. Please accept my apology --- most likely there is no such theorem, otherwise the reference would be already founded.
 A: Usually the strategy-stealing argument would go: suppose Black has a winning strategy. Then White can make an arbitrary first move, and then follow Black's winning strategy (with the adjustment that White makes an arbitrary move if the move White is suppose to make has already been played as a result of a previous arbitrary move).
However, this argument only works for games where playing an arbitrary move does not hurt you; this is not the case with chess, where zugzwang exists. So, the strategy-stealing argument does not go through.
It is mentioned in the answers to If there is a winning strategy, is it for White? that a proof of "White has a guaranteed draw or better" does not exist, and if it does, would be very difficult to find.
A: I think the real essence of the question is not so much in whether zugzwang exists in chess, but whether it exists in the first few (say 5) moves, and whether in that time white can effectively lose a move. I feel like the tree diagram for this shouldn't actually be that deep, if it's done in some clever way. You shouldn't have to do the whole game tree.
I'm thinking something along the lines of (assuming black can win), if the winning response to 1. e4 is e5, then the response to 1. e3 cannot also be e5, because then 2. e4 strategy steals. If you can piece together enough of those, perhaps you can prove that white can always strategy steal.
A: The type of strategy-stealing in chomp (mentioned by the OP in a comment) is exactly the one which could, in principle, be applied to chess: you don't want to neglect the first move because "it won't hurt", you actually aim at "reabsorbing" it so as to make W play exactly the same winning positions you are assuming B has at his disposal.
But, as it was said in the answer by ckefa, this, even if possible, would be very difficult. However the converse direction seems perhaps more tractable: is it possible to show that, if a winning strategy for B exists, it is not possible to steal it with W in the above-mentioned sense? For instance: if copying W moves as far as possible (e.g. 1. e4 e5 2. Nf3 Nf6 3. Nc3 Nc6 4.Be2 Be7 5. d4 d5 ecc... ) is the beginning of a winning strategy for B, it's plausible that it cannot be stolen by W.
(Of course this is of scarce practical relevance, because it seems so unlikely that B wins...but maybe it could be interesting for more abstract reasons).
