If an opponent attacks with a unit to an empty battlefield, can I use an action spell if it's not my turn?

Yes, you can use an Action spell when an opponent moves a unit to an empty battlefield, even if it is not your turn.

According to Rule 732.1.b, the Action keyword grants a card or effect permission to be played or activated during Showdowns, regardless of whose turn it is.

How the Interaction Works:

1. Showdown Begins: When an opponent moves a unit to an empty battlefield, a Showdown is initiated.
2. Open State: Because no chain exists at the start of this Showdown, the game is in an Open State.
3. Playing the Action: As long as the game is in an Open State (no chain exists), you have the opportunity to play an Action spell.
4. Chain Formation: Once you play your Action spell, it is placed on the chain, and the state becomes Closed. While the chain is closed, only Reaction spells can be played by either player until the chain resolves.
5. Resolution: Once the chain resolves, the state returns to Open, and players may again play Action spells if they have focus.

This is supported by the general mechanics of Showdowns, where players are granted the opportunity to interact with the game state regardless of whose turn it is, provided they have the appropriate timing (Action vs. Reaction).

Note: I could not fully verify this ruling against the retrieved rules.