Jet Blue has been pretty consistent over the years. Nonstop SYR to MCO is once a day first thing in the morning, and Nonstop return to SYR is late evening. Stops usually involve JFK though there are some other ways it can go (Boston, etc.).
Having done this a number of times (1 JFK layover and the rest nonstop) we do prefer the nonstop, even if it means early flying & late return. But we haven't been doing it with young kids either. Waking up at 2am to get to the airport for a 6am flight is tiring, but you do end up with a bit of adrenaline and can walk around a resort or park or shopping until the room is ready, then have a siesta, then go out for dinner (or, as we've done it, to an evening event like a Halloween Party).
JB's flights this year have crept down to 5am though, where my 2019 flight was 6:10am, 2018 was 7:20am, and my 2017 was 7:47am. The returns have been creeping later too. The 5am point means checking in at 3-something and it is a little ridiculous.