You don't have to put your floors on the ground, but they do need to be supported in some way.

I often put my starting shack up on a rock for the extra defense, then put the fire on the rock. Is the fire the reason why you are putting your floors directly on the ground? You can raise earth a bit for the hearth, and then elevate your floors on wooden beams. There is a button you can push to turn off snapping so you can set the height of the floor in relation to the beam manually.

You can of course flatten the ground with the hoe, fill in divots with raise ground and flatten lumps with the pick ax (not the same lump you just raised, unless you clicked twice instead of once) then do a second pass of leveling with the hoe to smooth it again. Repeat with adjusting and leveling until it's good enough. It's difficult to get it perfect, but you rarely need perfect when you are going to cover it with grass and building pieces. I rarely get dirt peaking through even when I do put my floors on the ground, and even then those spots can be touched up.