It was reported last week that the NFL schedule was set to release this coming Wednesday, May 15th. On Monday morning the league officially confirmed that.
As far as the official start time is concerned the schedule will release on Wednesday at 8pm ET, but if history is any indication there will be a number of leaks before that. Recently the league has also sprinkled official announcements for a handful of games in the lead up as well. This usually happens on a major program for the network in question (NBC’s The Today Show will announce NBC games as an example) and can also be expected between now and Wednesday evening.