Puerto Rico Atlanta Airport non-US traveler

So here is my question, me and my wife are both from Europe. We want to travel to Puerto Rico - which is sort-of USA.

First we do NOT have any valid US visa and as I understand we actually need one. That should ok - we can apply here, at home, for one.

My second and most important question is different. We plan to fly via Atlanta Airport and my understanding is that there's no such thing there as an international area. Meaning that when we get off the plane that arrives in Atlanta, we still need to enter the USA mainland territory (I really hope I am wrong here) - valid visa USA checks, etc. I've traveled to New York before and from my experience this can take hours (it took me 4 hours last time I was in new york).

So if there's a connection flight in Atlanta within these 4 hours for example, I can easily loose my flight from Altanta to Puerto Rico, right?

Any other pitfalls I might need to know? Thx!