I haven't been to SJU often, but I have been there in the early morning, before 6:00 am. It was surprisingly busy with pax for early morning flights. You should be safe, but uncomfortable. The first shops and restaurants I noticed opened at 6:00 am.
Stretch out on the carpet for a couple hours, if you dare. Have a leisurely cup of coffee and a pastry at 6:00 and take the 8:30 AA flight.