Sync several NC servers or share files over windows share?

So here’s the scenario, multiple offices (5) with 3-8 users per office need to share files.
Problem: Slow internet bottlenecks and slows down productivity.
Problem 2: Due to the amount of data 2TB+ we can’t install the NC client on each PC and have a local copy of the files.

My thoughts, installing a NC server at each location, users access files on their local instance which synchronizes with the others. As there normally isn’t multiple users working on the same file at the same time I don’t foresee delayed sync between servers due to slow internet to be an issue.

Optionally I was thinking setting up a NC server with all files at one office and a PC with the NC client at each of the others sync everything and share it, then map network drive to each user PC.

What do you all think works best if either or what other solutions might I try?