Not a solution to your problem, but you can press Ctrl+K to jump to the search bar, so if you press Ctrl+K before you start typing your search term it might be a little better until you can find a proper solution.

Hello Stretch78,

This add-on will do what you want - scroll down to 'About this extension', where it says :

"set the focus either to the address bar or to the web page (for example Google search field)"

https://addons.mozilla.org/en-US/firefox/addon/new-tab-override/

Also see :

https://www.reddit.com/r/firefox/comments/7ufqbg/quantum_new_tab_cursor_focus_issue/

Thanks guys.

So, right now there is no way of doing this within Firefox without installing an add-on?