Cold start problem on PK80S

Hi, so this is going to be my first post here.
I have a '82 PK80s which has been recently restored to some degree. Among other things it has a new SHBC 19.19 carb and a new piston with rings so as far as I can tell the compression is good.
It ran decently for two weeks or so, but now I ran into a problem when I can't kickstart it cold so I have to push start it instead. But when the engine is warm it starts like a charm from the first kick. I think it might have something to do with the carb setup, as it often cuts out when on idle, but I'm not really sure.
So maybe someone has any ideas what might cause this?
Thanks in advance!

Hi there,

Please also think of other possible reasons for your problem:

First thing I would do:
- Just fit a new spark plug. Even if the existent one is new, usual sparkplugs are not the best choice.

Then don't forget to check ignition circuit with a multimeter (red cable vs. white and green cable vesus white cable).
It can be possible that the CDI and/or the pickup has some minor failure. In this case it works above a certain rpm, but not below so you have to push start it.

...We would appreciate your response...