The earliest woven garment, at 5000 years old, comes from the site of Tarkhan in Egypt. It was excavated by my snarkaeological hero, Flinders Petrie (seriously, read some of the introductions to his dig reports where he complains about the French) in the early 1900s, but languished in storage at the Petrie Museum until the 1970s (bonus, that link also includes instructions for making a reproduction all your own).
Tarkhan featured some pretty impressive, large Early Dynastic tombs. Poke around the Tarkan link above to see some of the other finds and awesome stuff courtesy of Digital Egypt for Universities.
Even very early in the unification of Upper and Lower Egypt and various smaller power centers, the quality of production of linen and other items, as well as architecture is pretty impressive.