Yes, that's happened to me but more often than not, when life bumps, scrapes, or otherwise tries to pry off my sensor and bandage, my subsequent sensor readings remain unaffected. It's actually a sturdier situation than I at first expected. I do use Skin-Tac to help the sensor bandage sticker better and most people end up adding some adhesion help, even right from the start.
You can call Dexcom to report this failure but you'll need to tell them that the sensor was placed on your abdomen as that's the only FDA-approved site. They understand that sometimes sensors fail through no fault of the user and they are good about replacing them. If you nick a blood vessel and foul a sensor, they will replace in that situation, too.
I'm not trying to tell you not to use your arm. Many people exclusively use their arms successfully. I would consider beefing up your sensor bandage. Here's the latest Dexcom user guide and its advice for taping over a site.
It's bad luck that this happened on the first sensor. Don't give up! The CGM is one of the best tools we have.