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Should divine smite be declared before or after rolling and applying the melee weapon's base damage?

For example: a paladin and group have been ganging up on that session's miniboss and there's a chance the monster is hanging on by a low amount of HP. The group have also taken some damage, and the group are not in an area where a short rest is possible. The paladin has some spells slots left but has to decide whether to use them for smites vs. cure wounds for the group.

Can the paladin

  • swing his shortsword,
  • tell the DM the attack roll total and see if it hits,
  • then roll their 1d6 of damage with any mods and see if this mini boss falls over dead, and
  • if not then declare "and I'll add on a divine smite" as a bonus bit of hurt?

Or must they declare at the time of the attack roll: "if that hits I'll roll my 1d6 and these extra d8's from a divine smite."

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