Is there any way that surgery can help fix the damage from a stroke if it's done quickly enough?

No: Surgery can prevent more damage, but will not fix damage already present.

Thrombectomy: During the first few hours after a stroke, an acute blood clot (thrombus) in a cerebral artery causing sufficient obstruction can cause a stroke. If you are fortunate enough to live near an interventional neuroradiologist or neurosurgeon, a procedure removing clot from artery can be done.

Yes sometimes: When a stroke occurs, there can be brain which has a relatively low blood supply but is still alive and salvageable along with already dead brain. We call this salvageable region the "penumbra" and we can rescue this with a thrombectomy technique. Some patients don't have a salvageable penumbra and aren't candidates for thrombectomy. There are special ct perfusion scans we use to determine this.