Was the family of seven of nine the first humans to be assimilated in the 2350s? Was it because of them that the Borg first learnt about humanity?
Chronologically, no. The first humans assimilated by Borg were crew members of Picard's Enterprise-E on April 5, 2063 ("Star Trek: First Contact"); after the Borg jumped back in time to prevent First Contact between Vulcans and Humans as a result of Cochrane's first Warp flight, and Enterprise followed the Borg Sphere to prevent that.
Next incident was from the same time discrepancy - in 2153, the remains of Borg Sphere that Enterprise destroyed were found and thawed out Borg assimilated the research team
The next one was 2356 assimilation of the Raven, with Hansen family aboard.
More details on Memory Alpha: http://en.memory-alpha.org/wiki/Human-Borg_history