I haven't watched the documentary yet, but some quick googling suggests that it advocates for the early date of the Exodus (~1450 BC) compared to the late date (~1250 BC). First off, the phrase "accepted by most major scholars" is fraught with uncertainty in just about every historical discussion - professional academics thrive on proposing and advancing theories at odds with their colleagues/rivals, so you can find at least one professor at a legitimate university who says just about anything you like. In the case of the Exodus, the more "liberal" position is that it's not historical in the first place. Among more "conservative" scholars who do believe it took place, there are those in both the late date and early date camps.

As for archaeological evidence for the early date: it really depends on how you date destruction layers. First off, there's not a lot of physical evidence for the late date either. The archaeological record of Israel really starts around 1000 BC, around the time of King David. Before that, the Patriarchs before and the Israelites after the Exodus were still essentially nomads, living in tents and tending herds. It was a lifestyle unlikely to leave the kind of large-scale heavy footprint that archaeologists are able to find. Of course, there are destruction layers at many of the cities named in the Conquest narrative, but matching the relative date of excavation layers with an absolute date on the calendar is a tricky proposition. Some are claimed for the early date, some for the late date, while the skeptics claim they don't line up with either option. So there is archaeological evidence of a period of conflict that, depending on how one interprets and dates the sites, could line up with either (or neither) Exodus date, and could have been caused by the Israelites or a number of other forces.

There are other historical considerations, of course, but as you asked specifically about archaeology, the other item of particular note I can think of is the Mernepteh Stele, which I'm sure this documentary must mention.

Long story short, archaeology is a wonderful and powerful historical resource, but physical evidence requires interpretation to be applied, and this interpretation may vary widely between historians.