To be honest, it's a hard thing to properly research and date because garments made from natural materials tend to decompose.

Before we had the two needle knitting technique in Europe, people used hand knitting and single needled "netting" techniques to create socks. Also called nalbinding, Coptic-knitting, hand-knitting, cross-knit-looping, needle netting....there are a lot of terms and techniques. These techniques show up in Egypt, Peru, Scandinavia...all over the place, dated as early as 6500 BC (Israel) and 4200 BC (Denmark).

The nalbinding technique creates a very tight, flexible, dense weave that was super suitable for socks. There are different nalbinding stitches that involve back-to-front and front-to-back movement of the yarn around the thumb...and these allow more patterns and flexibility in the finished fabric.

Here are some nalbinding socks from Egypt dating between 250-420 AD : http://collections.vam.ac.uk/item/O107787/pair-of-socks-unknown/

Another example from the 3-4th century, just because I think they are SO COOL: https://research.britishmuseum.org/research/collection_online/collection_object_details.aspx?objectId=155676&partId=1

And here are some genuinely "knitted" socks that evidence use of double needles, again from Egypt, around 1100-1300. I mean, look at that intricate pattern...there's no way that was an art-form that had just appeared on the scene...so probably much earlier than this, really!: http://collections.vam.ac.uk/item/O128882/sock-unknown/

Knitting gets introduced to Spain and Italy probably around the 11th century and from here spreads across Europe. Here's a painting dated around 1400 that shows the Madonna knitting: https://commons.wikimedia.org/wiki/File:KnittingMadonna.jpg

Between the 13th and 14th century is when knitting really takes off in Europe, with knitting guilds appearing in France in 1268. According to Rutt, we have evidence of the purl stitch in the mid-16th century in Europe with the red silk stockings that Eleanora de Toledo, one of the Medici's, was buried in around 1562. The purl stitch was definitely popularized by the English in the 16th century, who were knitting stockings for lots of wealthy people, including kings!

Anyway, it seems that the purl stitch was known in middle eastern techniques but doesn't show up in European knitting until the 1500s. I included a link to Catherine Leslie's text below because she has a cool timeline that shows how the different techniques are evolving in different places, moving, merging, etc....

Leslie, Catherine Amoroso (2007). Needlework Through History

Rutt, Richard. A History of Hand Knitting. Batsford Ltd. 1987