Is it feasible for one person to level a 12ft wide concrete foundation slab on their own?
If you don't simply have the concrete company screed it for you (a good idea), hire a helper for an hour or two so you can screed sensibly from outside the forms. The difference between you walking down the middle of the slab and trying to fill your footsteps and them doing that is that they have some experience with filling footsteps when they HAVE to walk in it. But they'll almost certainly have two people screed it from outside the forms, and you should, too. Walking through it is not the preferred method.

As an aside, steel is cheap and easy before you pour, but essentially impossible to retrofit. Many home pours seem to skip reinforcement at all, which is penny wise and pound foolish. At least throw some 6x6 mesh in there, and bent #4 bars at the corners, tied to the mesh.