There can be no position where EVERY move by a side worsens its true value. This value is defined as the value achieved by the BEST possible move, which is the value the opponent can reach by their BEST possible reply (recursively).
There absolutely CAN be such a position. It is called zugzwang. But there is no way that white is in zugzwang at the start of the game.
You are in error.
If one side can FORCE the other into zugzwang (or another losing position), the advantage is there beforehand.
The thing to bear in mind is that in a tablebase, the value never changes when play by both sides is accurate. Note also that the only true values of a position in chess are white win, draw or loss. Anything else is an imprecise assessment.

While it seems very unlikely chess is a win for black, if there was a zugzwang in the initial position that required calculation to 500 moves deep to verify, we would have no way to detect it.
But it is very unlikely.