I first encountered XLR connectors in home audio with my Pass Labs Aleph P preamp, a product with was first offered in 1992 and revised in 1997.
The McIntosh C35 preamp sold in 1989-1992 had XLR outputs. For perspective, the preceding model C31V sold in 1987-1989 did not have XLR outputs.
XLR connectors had been in use in professional applications for many years prior, notably in microphone cables and powered speakers.
Your search for an integrated amp with XLR inputs might bear fruit focusing on those made in the mid-1990s or later.
The Luxman L570 class A integrated amp (2x50 watts) from 1989 has one pair of balanced inputs.