I can say that I pull several reports a day, for mortgages, not cars. But, 624 is not horrible or even real bad given the circumstances. Depending on who pulled your credit and which bureau (or all threee) you will get different scores based on the day they pulled it. It is only looking at the information that is out there as of the time that it is being pulled. The credit model for a car loan is different than a mortgage. Was your car paid on time? If so, they will probably weigh that more heavily.

Future planning - having everything paid off does not establish credit. Credit is 'getting something without paying for it' so if you pay for everything you will not re-establish credit. You just won't have any.