Gilgamesh Character Creation Quest
No sooner than I had a character on my guild's backup server, I was able to get in and create a Conjurer on Gilgamesh.
The server fix that Square Enix put in place, that required a shut down 9/3 to 9/4, was apparently successful in lessening the load on the servers. With the Gilgamesh server opened for the first time that I saw, I jumped at the opportunity and completed my first quest in FFXIV.
Now I can start exploration.