When was 1st Peter written?
According to the letter of 1 Peter itself, the author of the letter is the apostle Peter. Multiple sources, including Church historian Eusebius, tell us that Peter was crucified in Rome by Nero. We know that Nero was murdered in AD 67. Therefore, Peter was probably killed in about AD 65-66. That is the opinion of most scholars. The author of 1 Peter tells us he is writing from “she who is in Babylon” (1 Peter 5:13), which was, for the early church, a code-word for Rome. “She” would be the church in Rome. We are not sure when Peter ended up in Rome, but almost certainly not before the late 50s AD. Another clue is that the letter is addressed to the churches in Pontus, Cappadocia and Bithynia. These regions were evangelized later than Asia, Macedonia and Greece. This likely puts the letter of 1 Peter somewhere in the 60s AD. The most common date given is somewhere between AD 62 and AD 65.
Some have claimed that Peter did not write this letter. It is difficult to prove that he did, but the consensus of all the early church fathers is that Peter wrote this letter. For your information, there is considerably less confidence that Peter wrote 2 Peter, even among the early church fathers, but the evidence Peter wrote 1 Peter is fairly strong from the early church. So, with the proviso that we cannot prove that the apostle Peter wrote 1 Peter, but on the assumption that he did (which I personally believe), we can date 1 Peter to the first half of the 60s AD.