The engine could be stuck by the piston being stuck in the cylinder or the crankshaft is rusted and frozen or both of these.
Hopefully you'll get lucky and it's only the piston stuck in the cylinder.
There are several different ways to "unstick" a piston, most good. Here is the one I use.
Buy a bottle of Marvel Mystery Oil at a local auto parts store.
Remove the spark plug and elevate the front of your moped so oil can run down around the piston. Pour a couple of teaspoons of oil into the spark plug hole and replace the spark plug just finger tight .
Let it sit overnight or at least an hour or two.
After letting it soak and with the bike now level and on it's center stand, remove the spark plug and try pushing down on the pedal with your foot to see if it will break free. If that doesn't free it up put a 24 mm socket and ratchet on the front pulley's large flat hex head nut and see if you can turn the pulley Counter clockwise (left) to turn the engine and see if the piston will break free.
You can also push on the ratchet handle with your foot or tap it with a hammer.
Work the pulley back and forth a bit and then try it again counter clockwise.
If it doesn't break free try adding a little more oil and letting it soak again and then repeat the pedal push or ratchet/socket method.
You can also get a round wooden dowel a little smaller than your spark plug tip diameter and insert it in the spark plug hole and tap the dowel with a hammer to see if you can gradually force the piston to move.
Alternate the dowel and using the foot pedal or socket to turn the engine.
Hopefully it will break free. I also sometimes use ATF tranny fluid in a pinch.
You can also use the "Search" feature and search for "unstick engine" to see what turns up.