What time in the morning can consrtuction start in apartment complex?
That's a matter of local ordinance. You'll need to check with your city. It is sometimes modified by the construction permit process too, so you may need to check with the building department to see if the permit approvals specify a different time.
Construction start, stop and quiet days are covered by city or county ordinances, not statewide law, but I can tell you that 7:30 a.m. is not uncommonn. An ordinance might have a provision for longer hours in a genuine emergency. Many local ordinances can be found on line at the municipality's Web site.