Reconstituting genomes of archaic tribes of humans
The answer is basically 'No.'.

Too much mixing has happened since then. Fortunately, in most of the world we had scientists 2000 years ago describing facial features, and in part of the world (i.e. China) we had scientists describing facial features 4000 years ago.

We do occasionally recover viable DNA samples from both 2000 and 4000 year old corpses, also actual corpses that still retain significant vestiges of their facial features, but expecting to recover even general facial features over hundreds of generations from present DNA is quite frankly unrealistic.

The good news is that human facial features aren't actually super variable; humans are just super good at spotting small differences (which comes with the territory as social animals). The bad news is that as a modern reader of latin or chinese texts on phylogeny (if you can find them, which I won't guarantee) the subtle differences in what they mean when they describe a nose as, let's say hooked, will probably be lost on you, or me, or any of us.

Your best chance is probably sequencing corpses from the relevant era and matching them up with phylogenisists' descriptions to form an idea of what they were talking about; and you might end up with a general sense of what people looked like.

I expect it will lead to severely underwhelming results, but I suppose it's worth a shot.