Is there a way to make a country a puppet of another at game start 

Not right now, but it will come soon-ish (if not in the next update, it will come a week or so later).

Just note, the way subject nations work is that the overlord controls whether a nation is a puppet or not. So if you are thinking of making Poland a puppet of Germany, for example, you will want to have Germany set up on the site as well as Poland, when the feature is added.

cool thanks