ahhhhhh. glorious at&t glitches.
9 times out of 10 the physical SIM card is locked to the IMEI of the device it’s installed into and then that’s it, at least in that circumstance, so you would NOT be able to switch it out into your own cellular modem. You may not even gain anything from doing so, although that would be a possibility.
Even then, you are at the mercy of the BGW’s NAT table, and AT&T’s CG-NAT unless you can port forward, idk if passthrough would work or do you any good vs putting it in DMZ.