While we're waiting, here are some other questions with potentially relevant answers that address the origin of truly knitted socks and their earlier/contemporary alternatives:

• What was the sock situation before our modern ones?, answered by /u/thither_and_yon

• Something often repeated in the various knitting communities online is that the purl stitch was not known in Europe until the 1700s at some point. Is this true? Did people knit socks without purling? How so? And did they have a substitute for ribbing, purling between cables, and things like that?, answered by /u/LallaRookh

• When were socks invented or popularized, answered by /u/millcitymiss

• In "Mount&Blade: Viking conquest" Irish troops are almost all portrayed not wearing socks, unlike the Welsh, anglo-saxons, and Danes. Is this accurate? And if so why didn't the Irish like socks, answered by /u/Man-o-North

Not from one of the regions listed but seasonally still a cold climate, these socks from Egypt AD 250-420AD were made using a pre-knitting technique called nålbindning, which is also called single-needle knitting, needle binding or knotless knitting, although practically its more like sewing in that you weave the threads together with a single needle than casting off from two needles. It was used in Scandinavian countries and across Europe also.

You can see modern examples and help with the technique at r/nalbinding

Is nobody going to mention the best episode of the ask historians podcast??