From the Stack Exchange menu, I can scroll down to find a list of all communities, and I can use the search box there to find a particular community.
I'd like to have the keyboard input focus on that search box automatically when the Stack Exchange menu is opened.
I don't want the search box to come into view unless I start typing to search.
Compare: Windows 10 start menu. Just opening the start menu is enough to start searching on Cortana. You don't have to select anything. Just start typing and then Cortana will pop up with the results.
Just to be clear, I'm not referring to the search Q&A box. It can be easily accessed by pressing
S key if you have enabled keyboard shorcuts on your profile settings page.