alt Hacker NewsKolibriOS would fit in there, even with the data in memory. You cannot load it into the cache directly, but when the cache capacity is larger than all the data you read there should be no cache eviction and the OS and all data should end up in the cache more or less entirely. In other words it should be really, really fast, which KolibriOS already is to begin with.
Unless you lay everything out continuously in memory, you’ll still get cache eviction due to associativty and depending on the eviction strategy of the CPU. But certainly DOS or even early Windows 95 could conceivably just run out of the cache