How do you envision St. Antioch became the Bishop of Antioch, the largest congregation of Christians in the world at that time, which was filled with Christian who actually moved there from Jerusalem during the destruction by Titus?
Edit.
Scratch my last answer if you already read it. I see that I misread this. Notice that you refer to Ignatius as "St. Antioch," which confused me.
I don't doubt that Ignatius was a legitimate bishop in the sense that all other bishops/presbyters were throughout the decades leading up to his time, being one among many in Antioch, who distinguished himself among his peers. We don't have specific evidence, so we can only speculate how he distinguished himself. But it isn't difficult to imagine plausible scenarios. Most likely he and other like minded bishops/presbyters in Antioch recognized the need to present a united front against teachers they disagreed with, and provide clear boundaries between the churches in communion with themselves, and those outside that communion (notice that this, too, is a major concern for Ignatius in his letters, and is closely related to his insistence on bishops having the authority he wants them to have). In carrying this out as a college of bishops/presbyters in that city, they had to meet together as a group and work together in an organized way. As organizations generally require officers of some kind out of shear practicality, this college of bishops/presbyters selected Ignatius to fill a role that put him in a position of preeminence among them, perhaps as a presiding officer or spokesman. In fact, a development like this may have even happened before the time that Ignatius took such a position. Initially, this person would not have even been called "the bishop of Antioch." It is only after accruing more power to that office that it would be so distinguished, such that only that person would be the bishop, with the others being the presbyters.
We see something similar in the letter that is traditionally called 1 Clement, written perhaps 10-15 years earlier than Ignatius's letters. The letter only claims as its author "the Church in Rome," and as its addressee, "the Church in Corinth." It is traditionally thought that its specific author was Clement, whom later bishop lists call one of Rome's early bishops. But at the time the letter was written, it is clear that nobody was "the bishop of Rome," nor anybody, "the bishop of Corinth." But whoever wrote this letter from the Church in Rome to the Church in Corinth was, it was probably one of the bishops/presbyters in Rome, who was distinguished among his peers as the appropriate spokesman to write such a letter (and I don't doubt that this individual, indeed, was Clement). At this point in time (and even later when Ignatius wrote his letter to the church in Rome), the leadership in the church in Rome had not yet developed to the point of having a single bishop the way the churches in several cities in Asia Minor would soon have in Ignatius's day. But it had some of the circumstances in place that would make such a development possible. When Ignatius writes his letters to other churches in several major cities in Asia Minor (though not his letter to those in Rome), he is still laboring to persuade them to accept the authority of these singular bishops in those cities, as apparently they were undergoing the same process at that time as the churches in Antioch, most likely in an organized way under the efforts of Ignatius and his cohorts in those cities as a result of labors that must have been ongoing in the years leading up to his writing of his letters.
It is also important to recognize that the evidence we have from Ignatius's letters is his perspective on things. Out of all the Christians and churches in Antioch, we don't know how many recognized him as their bishop. Likewise with the churches in the cities to whom he addresses his letters, there's no telling how many Christians and churches there were in those cities who did not regard the individuals whom he calls the bishops of those cities as their bishops. In Ignatius's mind, those outside the authority of himself and the other individuals he calls "bishops," were not part of the true catholic church. But according to the Gospel of the apostles, he had no authority to say such a thing.