Athens Airport

Two hours seems pretty tight.
Your flight could be delayed for any number of reasons. You don't mention if you are checking a bag. I assume this is purchased separately, meaning the airline has no obligation to put you on another flight if you don't make it. Consider If you can afford the repercussions if you miss it. If not, then reschedule.
If it was booked together, I would risk it--I carry-on, use online app for check-in. On two separate tickets, this would be too stressful to me.

I wouldn’t do it. We had something similar going home from Rome after Sicily. We flew from Sicily the night before and stayed near the airport.

I would be more willing to do something like that if you were risking the flight to Santorini. But you are risking a very expensive transatlantic ticket.

We do have luggage so we would need to pickup in domestic and recheck for international. But I'm assuming that we wouldn't have to go through customs. I've read that the Athens Airport is easy to navigate. Anyone have personal experience with Athens Airport?

We flew Aegean from Thessaloniki to Athens and then EasyJet on to London. We only had carry on luggage and we allowed a three hour gap. The Aegean flight was delayed by 45 minutes and we ended up running through the airport with our luggage. We just made it but it’s not something I’d plan to do again.

Athens is quite manageable, as compared to Heathrow say, but it’s long and thin and there can be reasonable distances involved in getting from arrival to departure.

But I'm assuming that we wouldn't have to go through customs

Correct

BUT, .... you do have to go through Schengen zone exit passport processing and security after you retrieve and re-check your luggage.

You need everything to be the cliche of 'runs like a Swiss watch'.

If you miss your Delta flight I suspect the walk up fare for a flight the next day, if there is space, is not wallet friendly. Does Delta have more than one flight per day from ATH to your destination? How many is 'we'?

I would suggest getting a flight from Santorini the night before. If all flights are booked, you should take a ferry.

I have to go with Janet. We always make sure we are back in Athens the day before our return flight. We were on one flight that was delayed 3 hours from an Island. Half the pass-angers missed their return flight home because they planned to connect with their return flight.

Our flight from Crete was delayed for 1.5 hours. We had to rush to make our tour in Delphi but even had we been late, it is not the same as missing international flight.

There is an earlier flight arriving in Athens at 9:15. Our flight on Delta is at 1 pm.
Do you think that would work?

Yes the earlier flight is better. There is always a slight chance that there might be a flight delay like the one we experienced. However the extra time on the early flight is a better choice.