Around my state, the time to actually sign a lease for fall semester is at the beginning of May typically... the leases on most student rentals come up for renewal or end during May and landlords aren't going to wait for somebody just because they don't need it until August. Right now is the time to be looking at prospects and getting on waiting lists, so when (or if) a unit becomes available you're hopefully towards the front of the line.
Be suspicious of property management companies that try to rush you into signing, pressure is a tactic that slumlords use to keep you from looking around or researching them before you sign. Always good to find out names of the owner, management company, or whatever else might be applicable and search for bad press on the internet under all the different names. If you get a chance, chat with a current or past renter at a place you're interested in and ask if the place is maintained decently, if emergency maintenance problems (sewer backup, dead ac/heat, etc) are dealt with in a timely manner, and if the management/owner is reasonable (won't try to charge you for a new door/ac/plumbing if it needs repair due to normal age/wear as opposed to you beating it with a sledgehammer). I'd always had decent landlords and hadn't thought to do research, and then the last one I signed a lease with turned out to be the most infamous slum lord in town. We eventually ended up in court when I refused to pay an emergency plumbing bill and the jerk tried to evict me. The drains had been marginally functioning when I moved in and only got worse. The management office threw away all the repair orders I submitted, the only way that (or anything else) ever got fixed was to call the emergency handyman on a Saturday while the office staff was gone. I successfully defended my refusal to pay that bill and the judge was completely disgusted with the slumlord.
Some of the best landlords I've had were people I found on Craigslist that only own a few rental properties, so don't rule out classified ads in your search. Happy hunting!