i'd use the word simultaneous, in place of instantaneous. but whether it is actually simultaneous or not, is interesting to me, and i'm not sure about. i'd say, with your definition, and t being a time,
t(regeneration) ≤ t(belief)
that is, you have to be made alive before you can believe, because in unbelief, you are dead. so being made alive can't come after belief, but only before or at the same exact instant. depends on definition of 'belief' .. ?