After the preflop action completes, the remaining cards should all be re-shuffled immediately.

Interesting spot ... I like Suit's solution the best so far but I could tweak it as well, maybe. By using the would-be second burn as a Flop card we get 4 of the 5 natural Board cards with minimal 'work'. We take the pre-exposed Flop card and cover the stub with it until we need to put the Turn and River out, undisturbed.

This procedure is no different than what we do PF by using the first burn to replace an exposed card and covering the stub with the exposed card until the Flop comes out.

As an alternate you could do a second burn and put the natural Turn on the Flop, then put the pre-exposed card back in the deck for a reshuffle with resulting new Turn and River, as would occur in a normal pre-exposed Flop scenario. This gives you three cards unchanged.

Sometimes you just need to work on the fly. What if in OP's spot the Dealer had actually proceeded 'normally' but had only just turned over the three-card pile exposing only the top card? Is that any different than an accidental exposure of one card? GL