Institutions with pro-OA policies will either require their employees to shove stuff into their own archive, or they'll automatically crawl their staff's sites to add to the archives. Those archives are usually controlled by the same department as the university's library, people who already have some idea about preserving things for "hundreds of years from now".

In the UK the funding mechanism for (some?) academic research hinges on publication data so there's a rationale for bean counters to ensure the archive is properly funded - if you build this Open Access archive you get the data for your funding paperwork as an output. So this creates an incentive even in fields where Open Access is not normal.

(e.g. big swathes of Physics are OA, same in Computer Science, but for all I know Paleontology is a desert for open access)

You can publish in the conferences and journals, which maintain the archives and (I think?) still physically print and deposit in libraries of record.

But still also put the pre-print on your website.

the Internet Archive may prevent this from happening, despite retroactive robots.txt declarations and other such nonsense