Yes, DSL and a few others have a way to boot to a floppy then switch off to a usb in some cases.
Once in a while you can get slitaz to work like that too.
Might try plop.
Might be able to use pxe boot or a gpxe/ipxe floppy to boot to some local or network location. See www.netboot.me
and a fedora site used to work till they were hacked. A mirror of it is still up.
A built in CD ought to work but you may need to be create the cd carefully. Burn at slowest speeds and only with CD-R. A number of distro's offer a CD or netboot CD that can actually boot into a usb for files. Opensuse does that and others.