I think it's doubtful this sod, laid on only sand, will survive long
term. Turf needs some amount of decent topsoil and all this has is the
tiny amount that came with the sod. Even if it does survive, it will
likely present future problems, like needing a lot more water because
the sand will drain quickly. And grass in less than optimal conditions
gets stressed easier and hence becomes more prone to disease and
insects, etc.

I'd would definitely fertilize it now and using a starter fertilizer is
a good idea too, though not critical.