Background
Navigation keys (arrow, page-up/down) can be used to move element viewport, and user need to click the scrollable element to "focus" it.
However, the focus for this specific purpose doesn't seem to have a DOM interface.

Problem
How to set the initial focus programmatically?
Apparently, dispatching a simulated MouseEvent to another element cannot change this focus.

The solution is preferably for userscript, but if it is not impossible, a solution based on chrome extension is also acceptable.