Can a Black Mage/Thaumaturge become a machinest or dancer without being an archer?

[DefectiveMuse]

What has made you think Dancer and Machinist branch off of the Archer job?

The good news is that you're incorrect. Only one base class splits into two: Arcanist becomes Summoner and Scholar. And none of the DLC added classes (Dancer, Gunbreaker, (edit to add: Samurai, Red Mage), Dark Knight, Astrologian) have a base class. You will start Astrologian and Dark Knight at level 30 by default, (edit to add: Samurai and Red Mage at leveel 50), and Dancer and Gunbreaker at level 60.

Why not just start a new job as that thaumaturge? you can have every class on one character. And just buy a fantasia when you have $10, and boom you've got new race, new class, same story progression.

Though, of course, do what you want. I remade characters a few times too until I got tired of doing the early story, haha.