Collins:
hit it off - If two people hit it off, they like each other and become friendly as soon as they meet.
[informal]
They hit it off straight away, Daddy and Walter.
How well did you hit it off with one another?
[Also + with]
Synonyms: get on (well) with, take to, click [slang], warm to
https://www.collinsdictionary.com/dictionary/...

Oxford:
hit it off - (informal) Be naturally friendly or well suited.
The two of them hit it off wonderfully and it was the start of a great friendship.
It so happened that they hit it off immediately and became best friends off the court.
It wasn't long before all six of us hit it off, teasing and conversing like old friends.
He was glad his friends were hitting it off with Kelly, especially since the start of her day had been kinda rough.
https://www.lexico.com/definition/hit_it_off

M-W:
hit ...
hit it off - to get along well: become friends
they hit it off immediately
https://www.merriam-webster.com/dictionary/hi...

AHD:
hit - ...
hit it off - (Informal) To get along well together.
https://www.ahdictionary.com/word/search.html...

To me it sounds completely idiomatic to say 'They hit it off really well,' though of course only the first word is capitalized in an English sentence.

After all, you can ask the question 'How did they hit it off?', meaning how did they get along from the moment they met.

So in fact, I'm not sure about 'sich gut verstehen,' which is currently the only translation given in LEO. It's not wrong, but it does lack the component of meeting for the first time.

Oddly, the AE dictionaries fail to even mention that. At least the BE ones are more specific, so maybe their examples will also be useful.

Still, you can also use the phrase in other contexts, like 'We don't live very close to each other, but we always really hit it off whenever we can get together.'

Not sure if any of that helps.