@Juergen *****
, It's possible, but depends on the branches and the counter staff/manager of the branch (but not the bank). You may need to try several branches. There is no one answer to which exact branch would let you open.
It MIGHT help if you get a residence certificate/letter from your embassy (because you can not get one from most immigration offices on your visa-exempt entry stamp).
But opening a bank account is actually out of the scope of this group.
Please don't go further. This is already off the topic enough.