There is no documented way to change ownership of a bucket. To the contrary, the documentation states that bucket ownership cannot be changed.
Bucket ownership is not transferable
Even it were possible, that still leaves the issue of ownership of the objects in the bucket, since it is possible for a bucket to contain objects owned by a different account.
The bucket owner does not own objects that were not created by the bucket owner.
(It's technically even possible for me to allow you to create objects in my bucket, and for you to then set the permissions such that I can't even view the objects. My only possible action would be to delete the objects -- there would be nothing I could do, to change the permissions, if I initially allowed you to do this.)
So, barring an answer to the contrary from AWS support, you will want to work with the correct account from the beginning. You need credentials from the desired account with permission to create the bucket, if it doesn't exist, and at a minimum, permission to put new objects in the bucket. You likely will also need permission to list and get objects, for verification of your sync process and final results.