Just for fun))), a counter-question:
In chess (a turn-based strategy game), can black make their first move after white has already made their first move?

What do chess have to do with it? There are no restarts in chess. And there's no point in these restarts either. If a person is used to playing white, let's say, using the Sokolsky opening, they will make their first move B2-b4 a hundred times. Here, red doesn't so much make their move as see how generous the generator was to them. They then move on to a new map, not the same one. I agree with the previously stated opinion that red doesn't have that right, but the chess example, in my opinion, is not entirely appropriate.