I don't know if this is possible, but there's a separate problem to consider. Even if you can set your AT&T watch up without pairing it to a phone (AFAIK this isn't possible on the T-Mobile version, which is what I have), you might want to think about the battery life of the Gear S3 when it's in LTE mode.
The Gear S3 has great battery life for a smartwatch. When connected via Bluetooth to a phone, it turns off the LTE and WiFi radios, and gets over 2 straight days of battery life this way. However, in LTE mode it will get significantly less. Sometimes when I'm at work I leave my phone at my desk and go outside for a walk, and if I'm away for just 20 minutes, about 3% of my battery life is gone. Let's assume that 1% of that can be accounted for by connecting to the cell tower, and the discharge rate is 6% per hour. In that case, you've got about 16 hours of battery life. That's doable, and it's better than the discharge rate you'll get from your phone. But keep in mind that your phone can easily be recharged by USB charging ports, which are ubiquitous these days, whereas your watch needs a charging cradle to be recharged. Not trying to dissuade you here. I have a friend who used the Gear S2 (which has a worse battery life) as a standalone watch, and was able to get through a day with it. But he turned it off when it wasn't in use, which sort of defeats the purpose of a smartwatch.
Part of what makes the Gear S3 cool is its long battery life. I usually wear mine during the day and even to bed (it can track your sleep), and then charge it for 20 minutes when I'm showering and getting ready for work. The LTE connectivity is meant more as a backup data connectivity option than as a primary use case, for example if you go jogging outdoors or leave your phone at your desk when you're out at lunch. If you use it exclusively as a standalone LTE watch, I feel like you're going to be charging it too often to make it enjoyable or useful. Of course, if anyone has tried this and gotten better milage than me, please let me know!