I don't know if it is available to the public, but BATFE has a record of manufacturers licenses, and I think does put out a summary.
Trouble is that doesn't help too much as many manufacturer's license holders don't make guns. For example, many importers have U.S. facilities that are licensed as manufacturers for legal purposes but don't actually make anything. On the other hand, there are factories that make guns and are licensed, but sell only to one party which puts its name on the product.
If you add hundreds of gunsmiths who now have to be licensed manufacturers because they turn out a finished product from parts and pieces, not just repair or rework customer's guns, there are quite a few manufacturers who make very few guns.
LOL in your quest.
Jim