No need for stamping to get ssn.
You probably need ssn to work. You can start working when your H1B petition is approved, so apply for an ssn when your H1B petition gets approved.
Not sure what you mean when you say "resident" in USA, are you saying that currently you are residing in the USA (have some sort of visa) or that you are a premanent resident (which I guess you are not since you talk about H1B).