Sprouting plant time lapse - How would you do it?

Hello
I have been curious about how to simulate timselapse of sprouting plants like the very beautiful film below

I have seen some sophisticated demos for Houdini and maya based on procedural animation so I was wondering how it could be done in Blender. To animate the growth, I wondered how to do it using mesh keys but clearly I don’t have the level needed to work this out. So, How would you do it? (The ivy addon is not a valid reply as it does not sprout)

thank you