In addition to teleporting to an existing circle, the teleportation circle spell allows one to "create a permanent teleportation circle by casting this spell in the same location every day for one year." Is the teleportation circle usable as the designated destination for another teleportation spell during this one-year setup period? Or can it only be used in this way after the 365th daily casting that makes it permanent?
No, only permanent circles can be used as teleportation destinations
Teleportation circle says that only permanent teleportation circles can be used as an endpoint for teleportation via the spell:
As you cast the spell, you draw a 10-foot-diameter circle on the ground inscribed with sigils that link your location to a permanent teleportation circle of your choice whose sigil sequence you know.
The spell also says that until the last casting a year after the first one in the same place, this teleportation circle is not considered to be permanent:
You can create a permanent teleportation circle by casting this spell in the same location every day for one year.
So until that last casting the teleportation circle cannot be used as a destination.
However, do note that each day the circle is perfectly capable of providing 1-way teleportation to another permanent teleportation circle.
No, teleportation circle requires a permanent teleportation circle as its destination, and creating a permanent teleportation circle takes a full year.
The general rule is that spells do only what they say they do, and anything more is up to the DM. There are no "hidden rules." The description of teleportation circle, a link to which you've provided, supplies two possible effects:
Creating a one-way portal with an existing permanent teleportation circle as its destination, which last for one round; or
Creating a one-way portal with an existing permanent teleportation circle as its destination, which lasts for one round on each casting up until the last successive day on which it has been cast every day for a full year, whereupon it creates a permanent teleportation circle that can itself be used as a destination and lasts until dispelled.
Nothing in the spell's description permits the second effect -- i.e., the creation of a permanent teleportation circle that can be used as a destination -- short of the last successive day the spell has been cast daily for a full year.
Lest there be any doubt that the one-round portal created by either of the spell's two effects requires a permanent circle as a destination, the spell's description states that the "sigils" you use in the casting "link your location to a permanent teleportation circle . . . ." It goes on to state:
A shimmering portal opens within the circle you drew and remains open until the end of your next turn. Any creature that enters the portal instantly appears within 5 feet of the destination circle . . . .
Parsing that language, the "portal" that a creature "enters" is "within the circle you drew," which is explicitly distinct from "the destination circle." Ergo, the destination must be a permanent teleportation circle different from the circle you drew in casting the spell.
See also this question.
The teleportation circle is not permanent until after the last daily cast
It would only make sense if it only activated after the last daily cast as this is the condition for permanence.
The OP's linked spell description states that
As you cast the spell, you draw a 10-foot-diameter circle on the ground inscribed with sigils that link your location to a permanent teleportation circle of your choice whose sigil sequence you know
The spell description also gives instructions to create a permanent circle.
You can create a permanent teleportation circle by casting this spell in the same location every day for one year. You need not use the circle to teleport when you cast the spell in this way.
It is safe to say that if you miss just one day in this process, the creation needs to be started over. The permanent status of the circle isn't achieved until the last cast of a daily 1-year process.
As this is indeed ambiguous, I would consider the daily casting as the creation of this unique sigil sequence, and non-accessible during the creation of the permanent circle.