Typically that’s correct, but it can be done, it may stress the plant. If you’re careful it can be done with minimal stress.
I would go with the 2 gal pots, I start my autos in 5 gal pots. I have started them in peat pucks and then transferred to big pots.
So the one that’s just germinated I would put in the 2 gal pot now👍
When you move the ones in the solo cups, put the cup in the soil in the pot, at the right height, and moisten the souronding soil, then gently push the soil around the cup to firm it up, then pull the cup out so you have a perfect cup shape hole, cut the cup down the sides, so it can be removed easily, then just put the plant and soil in the hole