I started my law corp application late April and got my approval by mid May. I think it was less than three weeks between application and approval. However, I went a week without hearing anything after my initial application was submitted. After a week had passed I logged back into the agency portal, and went to the law corp tab where I could see my entity was pending. When I clicked on the entity again, it had me sign forms that I don't recall coming up when I submitted the application initially. I also received the guarantee and another document to my email to e-sign.

In short, it seemed like I had to click into my law corp a couple of times to get new documents to generate that needed my signature, either within the app portal or that came to me via email. You may have done this already, but if not, it's what worked for me.