Is there enough reaction mass on earth to construct a rocket capable of accelerating at 1g for 3.5 years?

No, it probably can not be a chemical rocket. Nuclear, yes.

My point is that we are in the realm of just needing new engineering (how to make nuclear reactions, or even antimatter-matter collision work for this goal), not new science (warp drives, something else we don't understand about space or gravity, or mass).