It would depend on if they have the contacts of your prescription in stock. If your eyes fit some average,it is possible that you will get them the same day. If it is the first time your wear contacts, the optomitrist will give you a pair of "tester" contacts and decide which type suits you best.
That will depend on whether the contacts of your prescription are in stock. If they have, then you can get your contact lenses on the same day. If they don't have in stock, then you would wait for 3-4 days to get your contacts back. Sometimes it would need a longer time. Maybe a week or so.