Molecular-level perception and control
One of the lesser recognized features of Maxwell's Demon is that if it can let molecules through a door, then it knows the direction that molecules are travelling in. It can therefore allow molecules to pass straight through in one direction, but not come back through from the other direction. Maxwell designed the thought experiment around heat - but it works equally well for setting up a pressure differential, creating a force in one direction.
If Superman wants to travel upwards, he simply causes gas molecules traveling downwards to pass straight through his body. (Compared to the body, air isn't very dense, and the worst thing that could happen might be slightly increased dissolving of gas in the blood.) But gas molecules traveling upwards bounce off him as normal. This gives a net upwards force, and he flies. Naturally the force can be applied in any direction, so he can just add easily fly sideways as forwards. No problems manoeuvring.
He can also fly in space. Molecular density in space is a lot lower, of course, but it's still there. Solar sails and ion drives demonstrate that small forces over a long time are perfectly effective to get around. And of course he'd use his exit from the atmosphere to set up his initial trajectory, so everything after that is just fine-tuning.
Edit: From a good challenge by @Trioxidane in the comments (thanks dude!) I've run the numbers for this. 1atm is 101,325N per square metre; let's round to 100kN/m^2. The frontal area of the human is approximately 1m^2 (Superman actively doesn't want to be streamlined for this), giving 100kN force. For a 100kg person and G of 10 (approximately), that gives us 1kN force from gravity. Then 99kN net upward force with 100kg mass gives you 99G acceleration! So Superman needs to be at least 1% efficient as a Maxwell's Demon to counteract his mass at sea level, and anything better than that lets him fly. At sea level, there's absolutely no doubt this would work (allowing for general handwavium of this in the first place).
The obvious problem with this is that atmospheric density drops as you get higher. Superman's limit for upward acceleration will clearly be 0.01atm, assuming 100% efficiency as a Maxwell's Demon. According to this calculator this happens at 16km altitude. This is lower than the flight ceiling of an SR-71 (25.9km), and isn't even close to space.
I also have absolutely no idea how this would work speed-wise. The speed of sound is, basically by definition, how fast air molecules can go. Once Superman reaches the speed of the air molecules, I suspect they can't push him any faster. So maybe his speed tops out at Mach 1, or maybe you skip over that particular wrinkle.
Whether these are obstacles to the story, or whether you can power though the plot so that no-one says "yeah, but...", that's your call.