Black is a crap shoot right now. It is very busy there these days. A friend of mine at the office went two weeks ago, showed up as a single at 3AM and the first available was after 1. Pre-Covid a single at 3AM was teeing off before 9. Also keep in mind that tee times are later due to daylight and you will be fighting darkness.
I would consider playing Red or Green if you were to go. I’m not too familiar with LI golf but the few times I have played out there, I wasn’t too thrilled. Bethpage always has good greens and fairways.
If you are willing to go at 10, I think you will be in good shape to get a reasonable tee time. If that fails, the Red or Green are good options.
Bring a blindfold and some ear plugs if you are looking to get some sleep because cars are constantly pulling in.