Was Ambrose really the first silent reader? Did everybody else really always read aloud?
Here is Augustine's description
Nor did [Ambrose] know my own frustrations, nor the pit of my danger. For I could not request of him what I wanted as I wanted it, because I was debarred from hearing and speaking to him by crowds of busy people to whose infirmities he devoted himself. And when he was not engaged with them—which was never for long at a time—he was either refreshing his body with necessary food or his mind with reading.
Now, as he read, his eyes glanced over the pages and his heart searched out the sense, but his voice and tongue were silent. Often when we came to his room—for no one was forbidden to enter, nor was it his custom that the arrival of visitors should be announced to him—we would see him thus reading to himself. After we had sat for a long time in silence—for who would dare interrupt one so intent?—we would then depart, realizing that he was unwilling to be distracted in the little time he could gain for the recruiting of his mind, free from the clamor of other men’s business. Perhaps he was fearful lest, if the author he was studying should express himself vaguely, some doubtful and attentive hearer would ask him to expound it or discuss some of the more abstruse questions, so that he could not get over as much material as he wished, if his time was occupied with others. And even a truer reason for his reading to himself might have been the care for preserving his voice, which was very easily weakened. Whatever his motive was in so doing, it was doubtless, in such a man, a good one.
No, Ambrose was not the first silent reader, there are plenty of other mentions of silent reading in classical literature. What Augustine found remarkable was not that Ambrose could read silently, but that he chose to do so--the classical ideal of intellectualism was not one of nebbish, shy bookworms who preferred to avoid the company of others, but rather of conversation, dialogue, public recitations and the like. A Roman intellectual was expected to be a highly public figure, who enters into debates and rhetorical display at the drop of a hat. Particularly a person of great social and political importance like Ambrose should not be reading by himself, but rather surrounded by a crowd of disciples, who might ask him question, challenge his interpretations, or simply sit in admiration at his learning. A clear reading of the passage makes it obvious that Augustine is not taken aback by any sort of literary virtuosity of Ambrose, but rather his inaccessibility, and from the context of Augustine's narrative this is meaningful as he is being pushed to violate his conscious for the sake of public office.
The whole idea of no silent reading in antiquity has a pretty interesting history but isn't a serious position and has been refuted numerous times.
One of the interesting things about Ambrose is the care that he took in his presentation. As Tiako has said, it's not the fact that he was reading silently that took Augustine by surprise, but the fact that he did so while having visitors waiting and watching him. I'm inclined to follow Neil McLynn's interpretation here, which presents Ambrose as supremely aware of the merits of his reception (McLynn, in "Ambrose of Milan: Church and Court in a Christian capital" depicts him as a "grand impresario"), points out the fact that Ambrose - who was not from a clerical background before his elevation to the bishopric - sought to present his own spirituality and learning on an elevated and separate scale. The inaccessibility that Tiako notes was vital in showing Ambrose as in some way beyond the disputes - such as his with Palladius in 381 - which characterised his first years as bishop. Separately speaking, many works in antiquity were read - and written to be read - out loud in a public setting; but this was more due to the availability of literature than to an inability to read without speaking.