Google Meet opens in a tiny side window,

and won't let me connect!

Ah, the dreaded side window! This is actually a shortcut called a Slide Over, and it is easy to fix.

First, put your finger at the top of the tiny window, and slide it to the right until it disappears.  

Go to Settings -> Home Screen & Dock -> Multitasking -> Allow Multiple Apps -> Turn Toggle OFF.  Then you can press the Home button to close.