Irenaeus 'Against Heresies'(AH), V, 28, 4, written circa.180 "As a certain man of ours said, when he was condemned to the wild beasts because of his testimony with respect to God: "I am the wheat of Christ, and am ground by the teeth of the wild beasts, that I may be found the pure bread of God.
Even if Irenaeus did not name Ignatius here, he must have known that according to "to the Romans" the alleged author is allegedly Ignatius, as written at the beginning of the epistle itself. And Irenaeus had good reasons to be unsure about "Ignatius" being the author. But "to the Romans" existed in 180 CE.
According to my study, the two mentions of Polycarp in "to the Ephesians" (21:1) and "to the Magnesians" (15:1) appear to be late interpolations. Also the epistle "to Polycarp" was probably written much later that the other six epistles.
One major reason for these deductions is that the epistle "to the Smyrnaeans" (Smyrna being Polycarp's city) does not mention Polycarp at all. But if written when or after Polycarp became bishop, the author of "to the Smyrnaeans"" would have Ignatius mentioning his name and even Ignatius meeting a young Polycarp.
My conclusion is that the six epistles were written before Polycarp became famously the bishop of Smyrna in his very old age, largely due because, as a young man, he was thought to have heard from the surviving Jesus' disciples or those who heard them.
And the Ignatian letters kept endorsing an early struggling unified orthodox church for each city, implying the catholic hierarchy was not well established yet.
Another thing is that "Ignatius" does not name the bishop of Rome, even if later on, at the end of the second century, a list of alleged very early bishops in Rome was existing.
For more details & justifications, see http://historical-jesus.info/ignatius.html
Anyway, from a lot of elements, I concluded the six epistles were written along within about 20 years, during 125 to 145 CE. "to Polycarp" was written much later, around 160 CE.
And certainly not by Ignatius", but by individual authors for each city (exception Rome), most likely a struggling "bishop" or presbyter who wanted to unite all orthodox Christians of the city under his authority.