No, PAN and Aadhar are mandatory as per RBI for online account opening. If you go to branch they would deny without PAN at first but they may open after filling form 60.
You can open a BSBDA Small account with a self-attested photograph and a declaration, but these accounts will have transaction restrictions and will be valid for 1 year until converted to full-KYC.
All banks must offer this, however branch staff will try to avoid opening this account, you have to insist, by talking to BM or follow the complain path etc.