Letters from Hittite archives have been interpreted as putting the Trojan War at about 1180 BC.
I’m glad that the synchronism — akkiyawa as Achaeans, a scattering of Homeric names — has begun to gain ground. Michael Wood’s “Search for the Trojan War” helped revive that I think, now it is generally accepted, as there were no counter arguments other than, ‘because I say so’ from some overrated overpaid gov’t hacks in the UK. It’s the age of those letters which has not been established, other than via the conventional pseudochronology, iow, the letters themselves haven’t been scientifically dated. A few years ago there was a published attack on the validity of thermoluminescence, and I suspect that will prove to be the opening salvo against another method which consistently undermines the pseudochronology.