If you can get to the floor from underneath, then driving screws from the bottom up would be preferable.
If not, then the simplest way is, as you said, drive nails from above. You can drive screws but the large head would require plugging the recessed hole with a wood dowel (to match your floor species), sanded down and finished to match the floor. You can use wood filler instead of a plug and get away with it, but it’s ugly.
If you can get to the floor from underneath, then driving screws from the bottom up would be preferable.
If not, then the simplest way is, as you said, drive nails from above. You can drive screws but the large head would require plugging the recessed hole with a wood dowel (to match your floor species), sanded down and finished to match the floor. You can use wood filler instead of a plug and get away with it, but it’s ugly.