Few thoughts on experimentation; Hair Length setting can be animated. So go from zero to full hair length. Hair material can be animated; the transparency of the hair-end can be animated along the hair to make it more visible as time passes.
That is an idea, but how to make it look more fluent and less stiffy?
I tried that (cant show you .blend file bcz its too large) it is quite good option, however I don’t have control over mesh, which looks very poor and fake. If I just could make hair mesh deform along curve.