This post is updated with graphic and links now that I've time-warped back to the modern era.
Katherine Gromer covers textiles from prehistoric Central Europe. One thing to keep in mind is that textiles very rarely survive in any form, so the first appearance of any technique will probably be very late and the estimates will be conservative.
Warp weights, cards, faunal remains, pottery impressions, stelae depictions, rock art, environment and sometimes rare fabric preservations create a limited picture of productions.
It's probably difficult to put hard and fast dates to any technique, but I'd guess twills followed wooly sheep into Europe as part of late Near Eastern population movements. Genomic analysis of ancient domestic European sheep will probably offer the best answer for length and coloration available at certain dates.
Card weaving is another story, but I think it may have been present in Late Neolithic Iberia based on depictions of stelae tunic belts and a broken item from Perdigoes that could be half a tablet (card) that has been otherwise interpreted as a loom weight. I'll write more on this with some examples and graphics.
It's not impossible that some of the zoned bands on Beaker pottery are schematic of card weaves (usually narrow like hippie guitar straps or the borders on hobbit clothes). The simpler diamond, triangle, zigzags and bordered-hashes might have alternated on zoned beaker pottery with very important plant schematics (probably for gruits: acacia, henbane and hemp) just guessing..
You'll notice that one of the most represented items of Late Neolithic iconography are men wearing elaborate patterned and colorful tunics.
Textile Society of America 2014 Biennial Symposium Proceedings: New Directions: Examining the Past, Creating the Future, Los Angeles, California, September 10–14, 2014 [Link]
For over a millennium, the site of Hallstatt, located in the Austrian Alps, was a meeting point between north and south, east and west, serving as a melting pot of new ideas and innovations. About 300 textile units (more than 700 single fragments) from Bronze and Iron Ages are known from the prehistoric salt mines, dating from 1500-300 BC. They display a wide range of textile techniques and provide insight in different aspects of textile craft. Their outstanding preservation allows us to investigate many crucial steps in the chaîne opératoire of textile production. The 2nd millennium BC is a time, when a lot of innovations in textile craft can be recognized, and Hallstatt offers some key finds. Recently, wool measurements were carried out, sampling not only Bronze and Iron Age textiles from the Hallstatt salt mines, but also skins found there. This enables us to study the development of sheep wool and its preparation techniques over a long period of time. This new data demonstrates that outstanding Bronze Age textiles also have specialized wool, although we do not know at this point if these textiles are imports or were produced locally. The Hallstatt finds are displaying novelties from the perspective of textile craft, such as earliest twills, dyeing, specific sewing techniques and the patterned tablet weave known in Europe so far. The occurrence of these techniques in the Bronze Age Hallstatt seems to indicate that it was an important transfer site for textile innovations. Bronze Age textile art clearly represents an invention phase, while these techniques developed and came to full use in the Iron Age, when we see them fully integrated into society. They influenced the social organisation, ideology and economy, especially of the representational culture of the higher strata during the Iron Age.