Question: I'm trying to do a search for `*40075*` inside azure folder search box, and was wondering how I can do a real wildcard search from the folder search box, and how.

Answer: 
Short answer, you can't. The "search" box is a prefix (starts-with) filter only.
This doesn't completely answer your question but it may help some folks including yourself. The **[Microsoft Azure Storage Explorer](https://azure.microsoft.com/en-us/products/storage/storage-explorer/)** desktop application enables a little bit more flexibility, but NOT MUCH. Overall, this is disappointing and inconvenient. Doing a wildcard search is a pretty basic file explorer feature and Azure Storage is failing us by not allowing it. This is now 5 years after your post and we still can't do it.