Absolutely. Pedigrees in rabbits are very different than say, pedigrees for dogs or horses. Rabbits don't get "registered" like dogs do, and all you need for a pedigree is an accurate family tree for that rabbit, basically. I think it's 3 generations? Basically as long as you keep recording which rabbits came from which pairings, after a few rounds of breeding you'll have a pedigree. Just keep meticulous records.
That said, just because a rabbit has a pedigree does not mean it is purebred or even representative of a certain breed. For that, you need to make sure you start with quality stock and keep breeding in order to achieve and improve your lines within breed guidelines. If you were to record all your breedings for several generations but your original rabbits were mixes of some sort and the rabbits you have don't match any one breed's standards completely... they're still mutts. Which can be great if you're raising them for meat, just understand that "pedigree" does not mean "show quality". Look at the individual rabbits for that.