Firefox also allows to search without bringing up the search bar first by setting "accessibility.typeaheadfind" in "about:config" to true.
Reducing the timeout for the search bar to disappear after the last keypress is very useful as well. This is hidden behind "accessibility.typeaheadfind.timeout".
Caveat: is messes with pages that use normal letters as keyboard inputs, like WASD as movement keys. One might need to disable it temporarily if that happens.
I use Firefox developer edition - I assume that's set up by default. Though I've learned to work around it, it has driven me mad for so long - I didn't know you could turn it off! Finally, it's fixed! Thank you!