Did Luke paint that picture?
It’s the “Theotokos of Vladimir” that some credit to St. Luke, some say that origin’s been disproved. It resembles th Black Madonna of Czestochowa said also to have been written by Luke as well as seven others by St. Luke and transported to India by St. Thomas before he was martyred there.
Luke is credited with being the Church’s first iconographer (excepting the ‘not-made-by-hands’ mandylion or Image of Edessa).
These icons are said to also bear resemblance to earlier paintings on cave walls.
Luke is reported to have first drawn both Mary and Jesus and to have done so at their home on, I believe, an oak table.
Icons of Mary and Jesus are relatively stable in the East, (see Christ Pantocrator) and medieval representations tended to follow these. The Shroud of Turin is also a close match in the case of Jesus.
So, who know, tradition says we have images/icons of Mary and Jesus from an early time. It may not be accurate to say “we don’t know what Mary (or Jesus)looked like.” Certainly, these icons would have the most provenance.