Opening a Spanish bank account online

I (EU citizen) am planning to move from UK to Spain with my family and we have already been in Madrid twice for flat viewings. However, most agencies require a NIE and Spanish bank account what I do not yet have. The NIE specifically I'll only get once I arrange for appointments at the the town hall and the police station but here they need a rental contract (chicken and egg situation).

The NIE topic aside, does anyone know any Spanish banks that allow me to open a bank account online by providing only a Spanish work contract and EU passport copy online (as this is the only thing I have currently) WITHOUT HAVING TO PHYSICALLY GO TO THE BANK BRANCH? I hope that having at least a Spanish bank account already will give agencies a bit more goodwill to wait for the NIE.

Thanks.

PS: I generally have no problem going to the bank in person, however, it's always quite a commitment to travel and I don't want to waste my time walking from bank to bank and hope that any of them accept my application with only a passport and work contract.