I've heard anywhere from 10 days to 2 weeks as the upper limit for what is considered "early", but I will say that an assistant dean of admissions at JHU advised students to get them in within a week.
I think your asking more like beginning of August?
I think at this point the faster the better but some schools don't send out II right away so those you could get away with a little more delay.
Thank you everyone who replied! Yes, I was speaking in terms of early or late August and early September, rather than days after receiving the invitation to submit a secondary application. Best of luck to everyone.