If a creature is given double strike after the first strike damage step, does it deal damage twice?

Double strike causes a creature to deal combat damage in both the first strike combat damage step and the regular combat damage step (CR 702.4b). However, a creature only participates in the first strike damage step if it already has first strike or double strike at the time that step begins (CR 509.1).

Here is the critical timing: after first strike damage is dealt and resolved, there is a chance for players to cast instants and activate abilities (CR 509.4). If a creature gains double strike during this window — after the first strike damage step — it is too late. The creature already missed its opportunity to deal damage in the first strike step, and it will deal damage normally in the regular combat damage step, but only once, not twice.

Conversely, if a creature with double strike loses double strike after the first strike step but before the regular damage step, it still deals damage in the regular step — it just loses the benefit of striking twice (CR 702.4b).

Concrete example: You attack with a 2/2 creature that has no keywords. Your opponent's 1/1 blocks it. In the first strike damage step, nothing happens for your 2/2 (it has no first/double strike). You then cast a spell giving it double strike. In the regular damage step, your 2/2 deals 2 damage and destroys the 1/1 — but it only dealt damage once total, not twice.

The bottom line: to benefit from double strike's two-damage-step effect, the creature must have double strike before the first strike combat damage step begins (CR 509.1, 702.4b).