No, no arrivals lounges in SYD. You will not be able to gain physical access to the international departures area, where all the international lounges are. You can get to the door of the Virgin Australia lounge in the domestic terminal (no boarding pass required to clear security in Australian domestic terminals), but I doubt they'll let you in without an onward boarding pass, and it costs AU$5.38 per person to take the train over there without a connection anyway. If you're staying in a hotel, they may be able to accommodate you early; guests arriving off of 20+ hour trips at 6:30 AM is completely routine there. (I can't speak from experience about a hotel in Sydney; never stayed in one.)

I personally go to the beach to wash off and get some sunlight to tell my body it's daytime. Water should still be warm in May.