If any necessary and non-substitutable material or equipment is based on petroleum chemistry, then we won't be able to do that. I'd love some nuclear engineering experts to chime in on it here; my uneducated guess is that it's extremely unlikely that there isn't a hard petroleum dependency somewhere in there.
The coal-powered steam locomotive era and the nuclear power era overlap. We almost did go from coal to nuclear. Especially in the UK, which had little domestic oil or gas in the 1950s.