Hi Maria and welcome to the community!
A branch is nothing more than a pointer to a certain commit in a Git repository. Git doesn't store locally any info on who created a branch (for branches created locally) and I'm afraid that Bitbucket Cloud doesn't show this info either for branches created from the website.
If the branches are always created by the developer who works on them, and if it is always one developer working on a branch (and not multiple developers), you may be able to infer it by looking at the commits of this branch (if there are new commits on this branch after it was created).
We have a feature request for displaying the branch creator on the Branches page of a repository:
The request has been closed because it is unlikely to be worked on in the near future. However, you are more than welcome to leave your feedback there, as our product managers continue to monitor even closed requests.
Kind regards,
Theodora
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