The Ramones and The MC5.
AnswerThis is a tricky question. As different people have different definitions of what punk rock is and when/where it began, there's no answer that everyone, or even mostly everyone, can agree on.
But I would say that the first punk bands ever were The Stooges and The MC5 in Detroit. A few years later, the first New York City punk band was The New York Dolls. Some might say it was The Velvet Underground, but this is a difficult opinion to maintain when you consider that lead singer/songwriter Lou Reed has consistently denied that his band was a punk band.
Either way, the Ramones formed in 1974, and the New York Dolls formed in 1971 (and The Stooges and The MC5 formed like, 5 or 6 years before that), so I don't see how The Ramones can be called the first punk band, unless you don't consider the Dolls or the Stooges to be "true" punk bands, which is a conversation that belongs on the Discussion page, not in this Answer box.