H1 and H4 at the same time

Hi All,
My wife will be coming for the first time.
She has H4 stamped first and then recently she got her H1B stamped.
So, when she is entering the US, can she choose which one she wants to enter on (H4 or H1).
If so, if we choose to enter on H4, can she use her I797 to get SSN and search for the jobs and can she convert to H1 while in US or does she need to re-enter into the states to get her H1B Activated?

Yes, she can enter on H4 with a valid H4 visa and change status to H1B. She can only get SSN once she is on H1B or if you have approved I-140, she can get H4 EAD and SSN. She will not qualify for SSN on H4 (with no EAD).
She dont need to go for stamping to start working on H1B once her status change from H4 to H1B in the US.

Thank you for the reply.

Please note she is never been to the US and she has both the visa stamped (H4 first then recently H1)