It should absolutely be possible. But it is often problematic to build older software because newer compilers are stricter on the syntax. But this is no definite show stopper since you can always install an older version of gcc. Which in turn will require an almost as old version, so you have to gradually work your way back (or take an easier way and download precompiled binaries).
I'm not entity sure of this but I think early versions of Linux had a boot loader built in so it could be copied directly to a floppy. So you can probably start it simply by using the kernel file bzImage (or whatever it was called back then) as a floppy image.