Getting the tree (at the root) is only a few requests (get the refs or HEAD, get the relevant commit, get the tree ID from that). If pack files aren't involved then that's literally 3 requests. Pack files make this more complex, but careful caching and range requests could reduce that to as few as around 5-8 extra requests (doing binary searching via HTTP range requests). I don't think even libgit2 has APIs for range requests on pack files though, so this would need a special library (or patching libgit2...).
There's also various optimizations on the git side like bitmaps[1] and commit-graphs[2]. If this a bare repo on the server side it shouldn't be a problem to make sure it is in a particular format with receive hooks.
That's just displaying a file listing though. Displaying what GitHub displays with the last change of each file is more complex, maybe the commit graph could be used so the client wouldn't have to fetch everything itself.
There's also various optimizations on the git side like bitmaps[1] and commit-graphs[2]. If this a bare repo on the server side it shouldn't be a problem to make sure it is in a particular format with receive hooks.
That's just displaying a file listing though. Displaying what GitHub displays with the last change of each file is more complex, maybe the commit graph could be used so the client wouldn't have to fetch everything itself.