Git cannot directly provide the precise branch creation date, but there are some ways to work around it so that it can be predicted more or less when it was born.
Here are a few suggestions:
Find the Date of the First Commit on the Branch
git log --reverse --pretty=format:"%h %ad %s" --date=local <branch-name>
Git’s reflog keeps records of the operations on the local repository that include branch checkouts, and branch creations.
git reflog show <branch-name>
In case your branch was pushed to GitHub, you can get the date of the first push to the remote and that will be the timestamp you are looking for. This is not the exact time of creation, but it gives the relevant hint as well if the branch was pushed soon after its creation.