Does the iPhone 12 Pro Max come with a SIM card?

Your new phone should come with a new sim card. In years past I would have said just transfer the sim from your old phone to your new phone and you'd be fine. With these phones having 5G modems, I would recommend using the new sim in the phone.

I just ordered iPhone 12 Pro Max and through the order my telephone number with AT&T will automatically activate on the new phone when I turn it on the first time.

You may not have ordered your phone to do that. My new phone is not carrier locked as I will not be under a contract to AT&T at all.

In most cases you can just move your old one to the new phone.

FYI, when we got the iPhone 12, we picked it up at the Apple Store and they advised using the new sim because of the new 5G chip. Whether that makes any difference or not, we did the same with the 12 and had it pre-programmed to migrate the partners phone number to the phone on turn on.

It was already installed in the phone. There's nothing to install. Either you have arranged for the sim to activate to your number on turn on, or you can simply call your cellular provider after you set up the phone to move your phone number over to the new phone. You can even do the activation yourself though your carriers website.