Not on a G3. These systems shipped with Mac OS 8; the System suitcase was over 6 MB alone. Apple stopped shipping systems with internal floppy drives altogether a few years later, with the iMac and blue-and-white G3.
You could absolutely boot a stripped-down Mac OS 8 on a floppy, including the beige G3. Apple even provided them ("Disk Tools").
Fascinatingly, the System file on the Disk Tools 8.1 floppy is actually a build of System 7, with HFS+ support grafted on.
didn't OS 8 come on a CD? I installed it from disc in my DVD drive. not sure how old you think the G3 is, but it's not as old as installing from floppy. just barely