Can I use my old sim-card in my new iPhone?

I bought a new iPhone 7 Plus today at an Apple store with AT&T carrier, unlocked, with a sim-card inside the new phone.

Unlike ordering one on the website, they didn't ask me for my phone number and the last 4-digit of account holder's SSN.

I went back home and setup my iPhone, but it had no service because I didn't do any activation. So I went to this att.com/activations to activate my phone, but it always says Looks like there aren’t any numbers eligible for activation on the associated account.

There's also another site of Gophone activation to activate by sim-card number and IEMI, but in the end it asked me to choose a rate plan, so I guess I was at the wrong place since I am in a family plan with my families now.

So I just pulled out my old sim-card in my old iPhone and replaced it into my new phone, and it is working.

I'm a little worried about it because I think normally I should use the new sim-card coming with the new phone. The old card works now, but will it have any problem in the future?