You might be able to animate a face extrusion in maya (by keyframing whatever value is attached to the extrusion) but at best it’d be a pretty inflexible solution.
Whenever I want to make it look like something is growing sort of magically along a path I just make the geometry and use an animated opacity map to do a slow reveal of the object. (the opacity map would start full black and then “grow” from one side across until it’s full white). The effect makes it look like the object is growing when really it’s just turning opaque.