Did Paul found the Church in Rome instead of Peter?

It’s interesting that someone would use Romans 15:20 against Peter founding the Church in Rome when the text seems to support it. Here’s what St. Paul writes:

I have fully preached the gospel of Christ, thus making it my ambition to preach the gospel, not where Christ has already been named, lest I build on another man’s foundation.

I can see how upon reading just this verse the reader might think that Paul was the first to preach, and therefore the one who founded the church in Rome. But verse 22 tells us the opposite:

This is the reason why I have so often been hindered from coming to you.

Paul had not gone to Rome yet because Christ had already been named there. And we know, from both Scripture and tradition, that Peter was in Rome. So it stands to reason that Peter was the one who laid the foundation in Rome.

For example, Peter sends greetings to his readers from “Babylon” in 1 Peter 5:13, which was a code word for Rome in the first century.

St. Ignatius of Antioch implies that Peter was in Rome when he writes in his letter to the Romans, “I do not, as Peter and Paul, issue commandments unto you” (Letter to the Romans, 4).

For a list of early Christian testimony of Peter being in Rome, see Jimmy Akin’s The Fathers Know Best.