I've never been out to Hains early on a weekday morning.
Are there any restrictions on what time the park opens? Any words of advice/insight would be appreciated.
No restrictions, although the gate may be closed if you get there early enough. No big deal, people just ride a bit on the grass to get around it then go on their way. Park police open it up sometime early in the morning.
As the weather gets warmer, club members will start meeting there at 6:30 am (some at 6 am), to do loops for an hour or so. The gates usually get opened around 6:30-6:45.