What is the origin of the use of “g” for a Riemannian metric?

I am asking about the reason for the use of this letter, if known, as well as the initial occasion of its use. Ideas that have been suggested concerning the former include:

• That it stands for geometry or Geometrie
• That it stands for some other German word
• That it is in homage to Gauss
• That it refers to Gravitation
• That it refers to the Gram matrix

As for the latter, I'm guessing it originates somewhere between Riemann and Einstein.

You are guessing correctly. Riemann did not use $g$ for the metric tensor, he writes things like $ds^2$ or $\sum dx^2$ instead, see his 1854 lecture "On the Hypotheses which lie at the Bases of Geometry" (1854).