Now obviously all my comments are from my experience in general but even my most water phobic swimmers have gotten that far after 10 weeks. As long as you make all of the lessons and try everything then you‘ll defiantly excel beyond that.
Within a 10 week program you will probably get as far as swimming for short distances [~10-15m] at a time, kicking on your front and maybe with arms. You will probably also be kicking on your back and maybe some arm strokes.
As everyone is individual you could conquer all or some of these or maybe excel beyond this. But floating and buoyancy should be the first thing you learn. That’ll comprise most of your first lesson – floating, body position and getting comfortable in the water.
Good luck and enjoy it.