Quite untrue. You can find about a thousand gun laws enacted between the founding of America and the 1934 act.
“Yet even now, far too few understand or appreciate the fact that though gun possession is as old as America, so too are gun laws. But there’s more: gun laws were not only ubiquitous, numbering in the thousands, but also spanned every conceivable category of regulation, from gun acquisition, sale, possession, transport, and use, including deprivation of use through outright confiscation, to hunting and recreational regulations, to registration and express gun bans.”
https://scholarship.law.duke.edu/cgi/viewcontent.cgi?article=4825&context=lcp