So technically starfleet encountered the borg early because of Q but also because Captain Picard did not turn back when he had the chance. He ignored Guinans warning. Yeah they might still have encountered the borg on the way back but Picard also mocked Q and his arrogance angered Q so Q sent them to the borg. So all of this is Picards fault as much as Qs. Yet Picard is still hailed a hero. Not sure if I agree 100% with that.
Prior to the ENT prequel, it was established that the Borg were already in Federation (and Romulan) territory, scooping up outposts like how we scoop what's in the kitty litter bucket. So they already had taken and figured out some Federation technology - the Enterprise being flung out by Q just hastened later events, though Q could be responsible for the Borg wanting Picard by name. Without Q, the Borg would have found some other human - but Picard was the first, as well as the commander of the Flagship, so it makes sense either way that he would be sought out.
I always wonder about the colony attacks in the season 1 finale "The Neutral Zone," where Federation and Romulan colonies on both sides of the Neutral Zone have been attacked. Nothing in the episode or in canon specifically states it was the Borg that perpetrated the attacks, or any identity given the attacker, but most people have went with the idea that it was the Borg who were responsible as a sort of initial raid of the Alpha Quadrant.
But it doesn't quite fit with the Borg to do hit and run attacks. I don't know, but it would seem more their style to stick and around and spread like a cancer, rather than to just gobble up a colony and run away.
Covert operations; even something as big a juggernaut as the Borg will still look up random bits and pieces surreptitiously to decide the best strategy in how to steamroller in. The fact that, in TBOBW, they send out one puny cube is telling*. The chance is low, but they don't want to reduce their numbly idly (or whenever at all possible) - unless it's the Borg queen in that one Voyager episode who's really that dumb to do so... the Borg exist to improve quality of life and their forces' strength (capability and quantity).
* to be fair, the fact that they have a time travel gizmo, which they use under the dumbest circumstances, with no tactical value or point, and only after sending ONE CUBE YET AGAIN**,*** yet they lose again. Why bother wasting drones when they could have used the time travel maguffin
before the big battle and from farther away, if preventing First Contact Day is such a big thing - why not go back earlier in time, never mind bootstrap paradoxes and predestination nonsense since the moment humanity is wiped out then the galaxy would be a much different place and Borgoshakespeare would not exist to write about it, either... Also: The Borg have no honor - Worf told us so, so it must be true. But even then, the Borg are about perfection and improving the quality of life (TBOBW). Again, wasting drones has never made sense
** since "adapt" means "let's try sending
two this time, instead of repeating the same failed tactics from before, and see if it works - one cube almost destroyed them all the first time and it's only by luck they figured out an unexpected weakness in time. And better yet, we intercepted a message that the dingdongs in charge are letting Picard waddle about in the Neutral Zone and we know where that is, uh-huh uh-huh. How'd they get to Earth so quickly like how TOS always had."
*** even VOY has the Queen telling Seven that they are sending x number of cubes to conquer one piddling species in one star system that doesn't seem too much more or less advanced and the Borg know the Federation is formidable despite already trying just the one... ugh!!