“We have no primary sources.”
Agreed that the Bible needs to be taken on faith, including on who wrote the gospels. But looking into the books and authors, there is evidence which backs up the accepted writers and dates.
One example:
The early church is unanimous in their acceptance of Matthew as the writer of the First Gospel. Papias, Irenaeus, Pantaenus, and Origen all report Matthew as the writer of the First Gospel.
Papias (c. AD 60-130) writes, “Matthew put together the oracles [of the Lord] in the Hebrew language, and each one interpreted them as best he could.”
Regarding the date Matthew was written, it was probably before 70 AD when the temple was destroyed as Matthew did not mention it.
Also - why make up a book and say it was written by Matthew? A tax collector of all things and hated by the Jews?
No, it needs to be taken on the fact that the books of the Bible were acknowledged by early Christians - dispersed across much of the world and by a Church that was picky about "correct teachings and interpretations" being handed down from bishop to successor.
as you point out - the early Church held to the writings of Mark, Matthew, John, Luke as written by who they said they were and this was acknowledged by multiple source
I would also point out that Christians OUTSIDE the Roman empire - the Marthomites of India and the Assyrian church under the Persian kings - they had the same books, the same beliefs and sacraments