Does Action Surge reset the Gloom Stalkers Dread Ambusher Attack?

If a level 2+ Fighter uses an Action surge would they be able to reset the Dread Ambushers free attack when taking an "attack Action" on their first turn of combat?

Dread Ambusher (emphasis added)

At the start of your first turn of each combat, your walking speed increases by 10 feet, which lasts until the end of that turn. If you take the Attack action on that turn, you can make one additional weapon attack as part of that action.

Action Surge

On your turn, you can take one additional action on top of your regular action and a possible bonus action.