You can nowadays look at a 3D-plot of internal density in an X-Ray computed tomography. On the chance that somebody mixed up an alloy that has the exact same density and X-Ray density as gold, you can try X-Ray absorption spectra which depend on nuclear resonances of different nuclei, so would conclusively prove presence and amount of non-Gold material.

And you can do activation analysis, where you activate the ingot with neutron radiation such that Gold isotopes form and decay. You then measure the decay gamma radiation spectrum and look for decay lines that are not gold but another material. This is non-destructive, but will make that ingot slightly radioactive for a while, but nothing that a few weeks of patience to wait for the decay can't fix.

Oh, and nuclear magnetic resonance (NMR) spectra would also work, but usually those machines are for very small samples in the milligram region. No idea whether there are some that could fit a gold ingot.

That wouldn’t work in Archimedes’ time because gold was the densest metal available then.

It could be done now but most of the candidate elements cost more than gold. Uranium looks feasible if the gold veneer will block the radiation which otherwise might tip off the recipient.

It stands to reason that people were not doing this though before Archimedes hit on density.

Only tungsten is cheaper and heavier than gold and it's tricky to work with