It is NOT like T5 at ORD. Int'l Terminal at ATL has no gates, just like the domestic terminal (or te

No. What if your flight is delayed. Check to see if your flight to Belize goes out from the new International Terminal. It's a seperate building and you have to take a shuttle bus to get there or walk through a long ramp. If you deplane, with your bags, you will go through security again, if the flight leaves from the new terminal. If your bags go through directly to Belize you should be ok. An hour is cutting it close especially if you need the new terminal. It's a huge airport with 7 terminals.
Even if your flight departs from the new Concourse F, there is absolutely no need to take any bus or go through security. Your connection is like a domestic one - just go to the new gate. Since DL uses almost all concourses at ATL, it may be a fairly long distance, and unless port of miami hotels you're going in and going out of the same concourse, you'll need to take the train between concourses.
It is NOT like T5 at ORD. Int'l Terminal at ATL has no gates, just like the domestic terminal (or terminals if you separate that structure into North and South) has no gates. All the concourses sit between the two terminals.
For Int'l arrivals, the procedure isn't much different than before, and anybody using ATL can't usually port of miami hotels avoid the train anyways. The big difference port of miami hotels is for those going into Atlanta. They no longer have to reclear security after customs. Now they can just exit to the outside world from the new terminal.
To OP - the problem with questions like this is that even if the consensus of the responders tells you a 1 hour connection time should be OK - if your inbound flight is delayed for any reason you may miss your connecting flight. If that happens you have to know what your flight options are in order to reach your final destination if your inbound flight is delayed. The point being, if the next flight to Belize is not until the following day you are going to be stuck at the airport and telling the airline that the responders on a Travel Forum told you it would be OK won't amount to a hill of beans - you'll still be stuck at the airport.