ATF Transparency Act This bill modifies procedural requirements related to the transfer or making of firearms that are subject to regulation under the National Firearms Act (e.g., machine guns, short-barreled shotguns, and silencers). The bill permits the transfer of a firearm if 90 days have elapsed since the application to transfer the firearm was filed, and the application has not been denied. Additionally, the bill establishes an administrative relief process with respect to an application to transfer that is denied. The bill permits the making of a firearm if 90 days have elapsed since the application to make the firearm was filed, and the application has not been denied. Finally, the bill requires reports on firearms-related background check inquiries that remain unresolved after 90 days and the percentage of firearms-related background check inquiries related to the transfer of a firearm that were administered by the Federal Bureau of Investigation.