MARTINSBURG, W.Va. — If there was one moment that summed up the current state of the Bureau of Alcohol, Tobacco, Firearms and Explosives, it was when the floor at the agency’s gun-tracing center caved in a couple of years ago under the weight of paper.

The accident was not entirely accidental.

The gun lobby, led by the National Rifle Association, has for years systematically blocked plans to modernize the agency’s paper-based weapons-tracing system with a searchable database. As a result, records of gun sales going back decades are stored in boxes stacked seven high, waiting to be processed, against every wall.

“We had a lady pushing a cart, and the floor just gave way,” recalled Tyson J. Arnold, who runs the tracing center, tapping the new, steel-braced deck with his shoe.

Now the long-suffering A.T.F. (somehow the “explosives” never made it into the abbreviation) is at the center of President Biden’s plans to push back at what he has called “the international embarrassment” of gun violence in America.