But so is the air at the surface, give or take some wind, and so are you. If you jump up into the air, which should meet the definition of "...not touching the Earth at all for even a second..." you have jumped into a volume of air moving at the same speed as the ground you just left, and you yourself have the same 1000 miles per hour speed as the surface you just left.
This is slightly misleading -- even if there were no air, we still wouldn't be able to jump and see the Earth rotate beneath our feet. Again, it's easiest to illustrate this by thinking of someone inside a train moving at a constant speed of say, 60 mph, going past a station at full speed. Someone at the station would see you moving past them at 60 mph. If, during this time, you decided to jump, you would see yourself go straight up and straight down, exactly where you landed. But the person in the station would see you still moving forward at 60mph as you jumped, so you would appear to trace out a parabola as you moved. From their POV, you wouldn't land in the same place you jumped from. (If the train were to suddenly stop at the station while you were in mid-jump, then you would continue moving at 60 mph relative to the ground
and the train, so you might collide forcefully with one of the walls.)
The same is true for the Earth. If you establish some coordinate grid where the position of the Sun is fixed, then you when you jump you would land at a different point than where you started -- but that's only because the whole Earth has shifted along with you. If you're familiar with vectors, you can imagine, just like in the train scenario, having a velocity vector of around 1000 mph pointing tangential to the Earth's surface, to which you're adding a tiny bit of upwards velocity. The net result is that the "x-component" of your velocity vector hasn't changed, so you won't move with respect to the Earth.