What's the absolute earliest I can get the Embroidered Tippet in Final Fantasy XII?

You can steal them from the Coeurls in the Tchita Uplands, which you must pass through just before the Sochen Cave Palace, which is just before Old Archades where you can buy them - but I do know I got one earlier than that, though I'm not sure where.

You can find Coeurls in Golmore Jungle as well, in the bottom-most part of the jungle just before you enter the Feywood, but you might not be able to handle the monsters in there after just coming out of the mines. (I probably got my first one there.) If you do go that route, keep in mind that clearing that area of monsters causes lots of undead to spawn, and they can slaughter you even if you had no trouble with the monsters that were present when you entered the area.

While this question was asked for the original version, this answer for both the original version and Zodiac Age version.

Original Version
In the original version, as Nickle states, the earliest point in the game you can get an Embroidered Tippet would be stealing them from Coeurls in either the Golmore Jungle or Tchita Uplands with a 3% drop rate. However, during the first visit to the Golmore Jungle, Coeurls will be significantly higher level than your party. So the likelihood of obtaining one then is pretty slim.

Zodiac Age Version
In the Zodiac Age version, you can obtain an Embroidered Tippet much earlier than the original version. On the way to King Raithwalls Tomb, in the Nam-Yensa Sandsea, a non-respawnable chest was added that contains this item.

Embroidered Tippets can still be obtained from Coeurls, but there is a slight change on how to get it. Rather than using the Steal technick, you must use the Poach technick. By doing this, there is a 5% chance you will get one.