T.S.
Usually with ANY new loan (car, house, personal) there will be a relatively "long" stretch between signing to loan docs and making your first payment. I assume this is what you mean by skip a payment even though nothing is really SKIPPED (ultimately you'll make EVERY payment until it's paid in full with interest) there WILL be a month where you are without a car payment (especially if you traded in your previous car so had THAT payment paid off on purchase day).
After the payperwork is processed, they have to give you a FULL billing cycle. So if you buy your car on May 2nd, and the company bill date is on the 1st of every month, then they start you on the NEXT full billing cycle and your first payment would be on July 1st at the earliest.
Check with your loan company and get the specifics for THEM but yeah, that's common practice.
HTH
T.