I open a new tab before I enter an address in;
if I use that, I have to move my hand to the keyboard, which take more time than moving my mouse up.
How often do you NOT type if you are opening a new tab?
If you are not typing after opening a new tab, then:
a) you opened a link in a new tab (no typing at all)
b) used a bookmark afterwards (right below the tabs)
Otherwise, you are going to need to type, as you stated yourself.
As for your mouse disappearing on ⌘ Cmd+T, looks like you Mac is broken. That is the right keyboard shortcut. You should use Windows!

And in general, GUI navigation is slow. I recommend trying to go a few weeks without a mouse as MUCH as possible. You might be amazed how much faster you can become leveraging your shortcuts.