When did they develop the technology to make tight socks? Did they make socks because their feet were cold or because of blisters? Was it normal for people to always wear socks with their shoes?
The history of tight socks is the history of stretch. All modern socks are made using the technique of fabric creation called knitting, which is done by hand with two or more needles and one continuous string of fiber/yarn; it can also be done by machine. Most stretchy garments are knitted; all t-shirts, for example, are machine knit. The reason for using this technique is that knitted fabrics, because of the way that the fibers interact, have a natural stretch to them that the fibers itself do not. Modern socks and other knitwear also almost always have artificial fibers like nylon in them, which is inherently stretchy and allows for a tighter clingier sock, but even a 100% wool sock has stretch to it and is comfortable to wear. The knitting is the key part. It also has the useful characteristic of being capable of complex topology, which means that you don't have to sew together flat pieces: you can make a piece of fabric without any seams that's got an inherent shape to it. As you can imagine, this is useful to cover feet.
Knitting is, however, a relatively modern invention. It doesn't appear much in the written historical record, but our earliest archaeological evidence suggests that it appeared around the 11th century CE in Egypt and spread from there. Earlier objects which you will sometimes see described as knitted were in fact made using one-needle techniques like nalbinding which are more difficult, less versatile, and less stretchy. (We know this because experienced fiber crafters are able to "read" fabric to see how the fibers travel over and under each other and understand how they're made.) There's just no way these were as common a garment as modern socks, though; they're not attested in the art and archaology the way they would be if they were.
So with the exception of those rare, laboriously nalbinded socks, how were soft foot coverings made before knitting? Well, there were things you could do to pad your shoes and absorb sweat or keep you warm, but I'd argue those things weren't really socks. Otzi, a man who lived between 3400 and 3100 BCE and was mummified in ice, was found wearing hay padding his sandals. Hesiod in the Works and Days advises, "Tie on your feet sandals made from hunted oxen skin, and under these, dress them with piloi," a word that comes from the word for "hair" and possibly referred to a kind of felt. You could also wrap your feet in leather, or fabric - the Russian military continued to issue foot wraps until 2013! But none of these are garments as we would think of them - they're just loose-ish material used to make you more comfortable. You don't fold them in your drawer.
If you wanted a SOCK sock, a reusable garment with a form, you had to use the two oldest forms of fiber crafting: weaving and sewing. Weaving creates a non-stretchy fabric on a structure that holds fixed threads vertically, while a long thread moves back and forth over and under them horizontally. Impressions of woven fabric have been found dating from the Paleolithic era. Sewing, using a single needle and thread to fasten together two pieces of fabric or hide, is even older and almost certainly predates the invention of spun fiber/yarn. European hose of the medieval period were sewn fabric, and so were Roman faciae. These originated as spiraling bands of fabric used as leg coverings, and began to wrap down around the foot to absorb sweat and friction. It's not a smooth linear history - leg wraps/hose meander up and down the foot and leg at various times and in various places.
Imagine your socks. Now take away their stretch. Now add extra seams that are going to rub your foot. Basically, we're talking about something constructed like a pair of khaki pants, INSIDE YOUR SHOE. Sure, hose became as thin and clingy as woven fabric could get in the medieval period, but you can't get past the fact that a sewn, woven sock is inherently uncomfortable. It's no wonder foot wraps were often preferred.
In the 11th century, true knitted socks finally show up, but they take a long time to spread. Again, they're found first in Egypt, which both seems to be where they originate and also has the climate to preserve them. The Virgin Mary was sometimes portrayed knitting in the 14th and 15th century - that's not a sock, but it's knitting in the round with double-pointed needles, which is the technique used for making a sock. They seem to have traveled first up into Spain from the Islamic world. Knitting was at first used in Europe only for luxury productions that involved incredibly fine yarn and gold and silver thread, and slowly filtered down to being a common householder activity. By the 19th century, women would walk around the Shetland Islands knitting stockings while they dealt with the kids and the farm so that they could sell them to passing ships for money.
Personally, as a knitter, I've often daydreamed that if I were sent back to almost any historical period, I could become hugely wealthy and famous with my skills. There are no myths about knitting, where there are a ton about weaving. And yet all the necessary tools were THERE for thousands and thousands of years, just waiting for the right technique to come along. Imagine suddenly encountering a stretchy seamless sock when you've never known one before! I have to imagine it would keep me in grain and beer for life.