Just to clarify, they can start to negotiate tomorrow but can not officially sign anyone until July 8th. But often news leaks out of that a deal has been agreed upon.
But I think it will likely be a few days before we even get that first confirmed signing rumor. These top guys are going to evaluate those 4-5 top teams for a few days at least, and some hesitation in Detroit, for example, could muck things up for a bit.