Emit smoke from growing curve

I have a curve which I animated to grow geometry along the curve via Object Data Properties > Geometry > Start & End Mapping. Works fine…
I wanted to use that growing curvegeometry as an emitter under Physics Properties > Fluid > Type: Flow, basically to emit fire from the growing curvegeometry.
However in the physics tab, of that growing curve, Fluid is not available.

How would I go about that?