It is effectively impossible, due to information theory. Effectively impossible, as in "heat death of the universe" becomes a legitimate limiting factor on your search.
You have a 2,000,000 byte (2MB) slice missing. A hash like SHA-1 has 20 bytes of information in it. By information theory, we should expect that there are 1,999,980 bytes which are still unknown. That means 2^(8*1,999,980) possible files to explore. That is a number so large that you start talking about heat death of the universe before every atom in the universe magically acting as a 2Ghz processor, working in tandem, could find it. And that doesn't include the challenge of actually figuring out which of the solutions is the right one. It's just the cost of eventually producing the right one.
Some have mentioned that you have additional information. For example, you have the SHA-1 of the entire file. Sadly, this is not very useful. Presuming you have this hash as well, you now have 1,999,960 bytes of information which are still unknown, and thus 2^(8*199,960) possible slices to consider. We're still in the heat death of the universe realm. We could add additional constraints, such as continuity with the existing video, but eventually we're going to run into limits as to how much we could possibly know about the slice without having enough information to just recreate it directly from the information we know.
The best chance you would have is to have the entire world all band together to solve your problem, and feed you every 2MB slice of data in the entire internet. It is highly likely that if you "lost" the data, someone else might have a copy of it. It's much easier to scan through the petabytes of data humanity has gathered than to can through the far larger number of possibilities 2MB of arbitrary data has to offer.