Xiongnu tribes continued to raid Northern China in spite of Han paying tribute regularly and marrying off imperial princesses to the leader of the Xiongn

I mean, when in the 350 year history between ascendant Xiongnu and their demise are we talking?

The only true lasting peace between the Han and Xiongnu came when the Han cut off the the Xiongnu from all their sources of tribute, and effectively caused the confederation to collapse and the tribes to descend into internal conflict.

That's a very reductive outlook, given the two populations had an on-again-off-again wars going back for the duration of their existence. Either way, components of the Great Wall already existed at the time of the conflict and did little to mitigate it.