But the Borg were already active in and around Federation space prior to Q Who, such as those outposts destroyed around the time of the episode "The Neutral Zone". You could justify what happened by assuming that the Borg destroyed those outposts because they assimilated Seven's parents' ship and decided to probe these new species they just learned about.
You could also say the Borg decided to probe these new species after the transmission from "Regeneration" was received in the Delta Quadrant. Once they found out that some Borg had, without the Collective's knowledge, been at the location of Earth in the 21st and 22nd centuries, they decide to give the situation a closer look.
The whole Borg story arc revolves around a predestination paradox. The Borg wouldn't even be interested in Humans if their interest hadn't been aroused by a 200 year old message they received from themselves. In "Dark Frontier" the Borg Queen flat out says that humanity is an unimpressive candidate for assimilation. That's why I believe they didn't go after all of the race after the Hansens were assimiliated. They're interested in humanity, and other nearby species, because their own time travel paradoxes have caught their attention.
The "first contact" between the Borg and the Federation at the hands of Q in "Q Who," then, isn't what it appears to be. It was a situation where the Federation "officially" met the Borg for the first time. However, the Borg where aware of humanity's existance long before Q introduced the Enterprise-D to them.