I think it is an instant approval. If you have provided the right documents, pictures of ID verification are clear and correct, you will get your wallet enabled instantly. So you can then deposit and begin your journey at stake.

It's most definitely not instant everytime and this logic applies to literally any site out there. Some sites process the information quickly as long everything is legit, but some sites take a lifetime citing various reasons.
Stake is no exception. It comes down to the agent handling the processing basically at the end of the day based on what I observed.