What to do about sellers on internet auction sites who say a gun is an antique and no FFL is required, but there is no proof that the gun was made prior to 1899?
What to do?
Easy. Ignore them and let the ATF worry about it.
FWIW the line defining an "antique" is not always clear.
Although reference sources often claim that a specific serial number is the cutoff between one year's production and the next, collectors have often found guns that turn out to have been built in the "wrong" year when a factory history letter is obtained. Many 19th-century industries used a business model that was quite the opposite of today's popular "fast turnaround - minimal inventory" philosophy; it was not uncommon for manufacturers to accumulate vast stockpiles of extra parts for future production, so items like guns were often assembled out of serial number order.
The production year for legal antiques has been interpreted to be the year the serial-numbered part (e.g. the frame or receiver) was built, which is NOT necessarily the same as the date the gun was assembled and shipped. For example, S&W famously built enough frames in the early 1890s for their .44 Double Action top-break revolvers that they were able to produce the unpopular model until 1913 using parts from inventory (see above). Every .44DA is considered an antique, even though IIRC about half of the total production was assembled in 1899 and later!