I know for me, if an adopted pet's information was not available for some reason, or if there was a big delay in getting it, I'd have to treat the it the same way I would a stray, and take it immediately to the vet. In my case, and probably others' as well, that means before it even comes home. This is not just for the adoptee's safety, but also the safety of existing pets. I have an entire folder full of documentation that was given to me the day I adopted my cat from the shelter last month. Shelters sometimes have the adopter sign a contract that the cat will be spayed/neutered before a given date if it hasn't already been done, so you probably want to have any of the contractual paperwork as well.
People keep bringing up shots to me, and I am contacting the place where I got her to see what she needs. All I know is that she was dewormed the day I got her. I will also talk to the vet. She was a Christmas gift, I don't know every exact detail about where I got her.
One other thing, when asking the place where you got her what she needs going forward, also ask for everything she already had done. Ask for specifics (exactly which vaccination, etc) I know it sounds redundant to do that, but your vet will want to know what she's had done, the dates they were done, and all that good stuff.
And we just want to help you, and Franky, who is seriously adorable, have the best life together possible.