We do not know. No one knows. The tradition that it was Peter is open to all sorts of discussion. The Bible gives Paul a much stronger, clearer connection with the church at Rome than it does any other apostle.
But what difference does it make who was the first bishop (or elder, for so it means) at Rome, not of Rome? A vastly more important query is, Who is the head of the church of God, the true church? And the Bible answers that very clearly: "And hath put all things under His [Christ's] feet, and gave Him to be Head over all things to the church, which is His body." Eph. 1:22, 23. "He is the Head of the body, the church." Col. 1:18. Not only this, but there are no intermediaries; for "the Head of every man is Christ." 1 Cor. 11:3. "For other foundation can no man lay than that is laid, which is Christ Jesus." 1 Cor. 3:11. See also 1 Peter 2:4-8. As to primacy, or headship, among the apostles, Paul tells us that "he was not a whit behind the very chiefest apostles" (1 Cor. 11:5), and when he mentioned the apostles, with this very matter of leadership in view, he places the three great apostles in this order, James, Peter, and John. Gal. 2:9. Furthermore, the first council that was ever held, the only apostolic council, was held in Jerusalem, and the divinely appointed president, chief spokesman, of that council was James. Read the record in Acts 15:6-29. It was Jesus who said, "One is your Master, even Christ, and all ye are brethren." Matt. 23:8.