"Our relationship is starting to pick up". Does it sound natural?
Meaning the relationship is beginning to get more intense, to unfold etc.

What's the more native and colloquial way of saying that?

Question

"Our relationship is starting to pick up". Does it sound natural?
Meaning the relationship is beginning to get more intense, to unfold etc.

What's the more native and colloquial way of saying that?

Answer

Your description using intense is good.
Our relationship is ...
getting (more) intense.
getting closer
We are ...
getting closer.
growing closer.
falling in love.
clicking.

Answer

Your sentence sounds natural and it could mean what you suggest but is could also mean that your relationship has not been so good, but now it is improving.

Our relationship is starting to get serious or  our relationship is getting serious, does mean getting more intense etc.