Depo-Provera - 1st timer -Can the shot stop your period right after you get the shot?

Your periods can stop immediately, or in days, weeks, months or not at all. Everyone is different.
Most likely you'll find they'll stop & start over the next year, as your body gets used to the artificial hormone. You may also get other hormonal symptoms. Weight gain is common, so having a good diet & exercise regime now, could really benefit you.
The Manufacturer advises that you should not use Depo Provera as long term contraception (longer than a couple of years), unless you feel you have no other choice. If you feel that lack of options applies to you, then they advise you take regular breaks (every couple of years), to help avoid unwanted affects on your body, such as bone thinning etc. If on it long term they recommend you have bone MRI scans to check for that particular disease (osteoporosis). I had one recently as I was on it 18 years with regular breaks & taking healthy bone supplements.
It is common to take up to 18 months to get your fertility back after missing your Depo shot, even if you only had the 1 shot (quote from Manufacturer). However, technically, pregnancy is possible for some women as soon as 13 weeks after the last shot.
If you haven't already, I suggest going to the Manufacturer's website & reading the information on this Drug.