Prove it!
I can prove there were Churches all over the landscape. Proving what epistles they had, and when they got them is gonna be a might trickier.
Because each and every Epistle SAID SO. Example:
I Corinthians 1:2 - To the church of God which is at Corinth......
II Corinthians 1:1 - .....To the church of God which is at Corinth with all the saints who are throughout Achaia:...
Romans 1:7 - ......to all who are beloved of God in Rome, called as saints...
Galatians 1:2 - ...........and all the brethren who are with me, To the churches of Galatia:
And on and on it goes. These books were LETTERS sent to the various churches by Paul, or Peter, etc. Unless you're going to call God a liar the burden of proof that they DID NOT HAVE THEM is on you.