No, we wouldn't say that. We would always phrase this statement as "I don't think we've met before". Or, if you wanted to say 'we've not met before', you'd use a tag question: "We've not met before, have we?" If you were to say "I think we've not met before" people would understand you, but it would sound strange and unnatural. A general rule is that we always put the negative element as near to the beginning of the statement as we can.

"I think we've not met before" is formal and less said. The 2nd is more idiomatic and far better to say if you want to sound natural.

the first option sounds more british. they use "have" in "-'ve" more often. it's unusual to use the negative like that in american english at least. much more common to hear the second

Thank you very much, Trisha!

You can and will be understood by English speakers, but it sounds quite formal. "I don't think we've met before" is much more common.