starting blog at beginning

I understand that the post loop is going to (at least by default) show the newest posts first, so they are in reverse-chronological order.

I’d like, however, to create a link which would take someone to the first post within a category, such that the posts_nav_link() would allow them to navigate through the posts in chronological order. So far I see how I can link to a Permalink specifying the single first post, but then my navigation aids don’t appear because the loop is constrained to the Permalink.

This seems like something that must be possible — certainly for some blogs it makes sense, at least on the initial read, to start at the beginning and not the end.