If you're not averse to public transit, you could take the Metrolink commuter train which starts running at O'Dark Thirty. It terminates at the historic LA Union Station and connects there with the subway, the
Metro Red Line (and I see they've renamed that to the 'B' Line - whatever). The Metrolink round trip fare does include the Metro fare, but pay attention to the return trip schedule - it doesn't run real late, but if you "rope drop" Universal you won't be there late anyway.
I
presume there are breakfast options in Universal Citywalk that would be open before USH.