New college grad and I got my first job offer but I hate not knowing what’s going on

So basically I got a job offer at the end of March and I accepted (electronically) also electronically signed the employee agreement. I emailed HR to let them know I accepted and I was told congratulations and that on boarding would be in May. I haven’t had any communication since then and I’m wondering if I should contact them to see what’s up or wait till the month is over ?

Also Im new to working and I accepted to let them do a background check but I have no idea how it’s conducted or when it’s concluded. I don’t even know what information I was supposed to give them aside from my social?

Just some info and feedback would be nice.

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