How do I make a turtle egg-like block be spawned from breeding, and then hatch?

I've recently been experimenting with breeding, and while it is pretty limited, I believe this should be possible depending on your exact preferences. 
Some things to note:

• Based on my tests, the "breed" AI block is the ONLY way to get entities to enter 'love mode' and path find to eachother reliably
• Upon successful breeding, entities will ALWAYS spawn another entity of the same type with its 'Age' NBT tag set to child (negative value)

So what I recomend is to make an update tick procedure for your "desert rain frog" and have it detect if it is a child (this block already exists, just search "child"). If the entity is a child, immediately despawn the entity, and place your burrow block underneath it.
(This is very similar to what I've been doing, except I spawn in the baby entity instead of a custom block)

You could also run checks so it only places the burrow if on sand/dirt/etc, and maybe even have a special 'digging' animation play when your frogs stand on the burrow  using geckolib plugin.
 

Hope this helps!