No known atom has electrons in a g orbital in the ground state, but that doesn't mean that g orbitals don't exist. Electrons can occupy g orbitals in an excited state.
Currently recognised elements go up to 118 (oganesson), with complete 7s, 5f, 6d and 7p shells. Once you get beyond that (if you do), you will start filling up 8s, then perhaps 5g, etc.