The Borg didn’t suddenly expand so quickly so much as they recklessly ventured into new territory looking for where the Humans came from.
In RTS terms, the Borg “turtle.” They build up within the safety of their established territory and deploy slowly to avoid sudden losses.
Seeing the Enterprise-D and realizing it was very far from home made them rethink their doctrine and began quickly pushing into the Alpha and Beta quadrants to relocate them.
This caused them to encounter thousands of new species in a very short period of time. They definitely took ships and colonies along the way (that’s why those Romulan outposts disappeared, just one more new species they ran into while searching for Humans) but they didn’t stop to completely conquer all of those species like they had been doing in the Delta Quadrant.
Funnily enough, the only Borg ships to ever enter Federation space or reach Earth were scouts (save for the Queen’s failed Hail Mary run while pursuing Voyager). The Borg never actually swarmed humanity, there would have been no stopping them if they had.