Few questions that might not determine why it’s not starting but important nonetheless:
1) Did you get a new head as well? It should match the diameter of the cylinder.
2) Did you set your ring gap?
3) Are you using a needle bearing on piston/con rod?
4) Did you reuse your wrist pins on the piston? (never do this)
5) Did you properly torque your head bolts to 7ftlbs? (standard for Puch)
6) Did you buy a temperature gauge?
7) Did you rub a lil 2stroke oil on the piston/walls when installing as not to scratch either surface?
According to Freds Guide the 3 things you need to start a moped are spark, compression, and fuel. The thing you’re most likely changing is compression, but as we all know, it’s a lot more complicated than that.
What do you mean your moped won’t start?
Do the pedals lock up?
Can you spin the flywheel freely?
Have you checked for spark with the kit installed?
Forgive me if these are basic and redundant questions/advice, but from your posting it sounds like you’re trying to plug-n-play without much heed for any of the many intricacies of kitting a bike.
Post pictures (of the bike, cylinder, head, flywheel, etc.), those tend to help a lot and may even help somebody trying to help you discover something else entirely wrong with your bike. Hope this helps!