Augustine's anecdote about Ambrose, which the article begins with, is often misinterpreted. It's not that Augustine was amazed at Ambrose's ability to read silently, but rather that he did so in front of guests. That he remarks upon Ambrose doing this points more to it being a faux pas to not share with guests what you are reading rather than it being an extraordinary feat.

Augustine himself writes in Confessions about silently reading a book that would spur his conversion to Christianity:

I snatched up the book, opened it, and read in silence the passage upon which my eyes fell...

This question does come up pretty regularly in AskHistorians:

https://www.reddit.com/r/AskHistorians/comments/3382rr/was_it_really_considered_rare_and_impressive_to/

Edit: Fixed spelling error.

While people may have been capable of reading silently before the Middle Ages, it is generally regarded by historians of reading to be a reading strategy which emerged in the Middle Ages, and did not become the norm for all readers until the fifteenth century. Firstly, silent reading is actually a skill. Before it could occur, people had to learn how to read without pronouncing the words they were reading. Different groups of readers mastered the technique at different times, beginning with copyists in the monastic scriptoria and scholars in universities in around the twelfth century. They were followed by the aristocracy.

It is considered revolutionary in its effect on reading practises, as it allowed reading to become a more intimate activity, and affected personal devotion in particular. Many mendicant orders relied heavily on silent reading for personal devotion. Additionally, it allowed for the secret reading of heretical ideas and well, things not meant to be read communally. It was a new method of reading, but it overlapped and coexisted with other forms. Reading aloud with others for work and pleasure was a common way to read, and it continued alongside silent reading. However, by the sixteenth and seventeenth centuries, there was a division between those that considered reading a communal act, and those that thought of it as private, as the latter relied on a higher skill of literacy. Silent reading allowed for the privatisation of reading, which Chartier, and many other scholars, consider one of the major cultural developments of the early modern era.

(Sources: Roger Chartier “The Practical impact of Writing” (1989)

So, I can speak to the ancient Near Eastern aspect of this--there is actually a decent amount of recent secondary literature on the subject. I'll give a couple of primary examples for now, but the literature on this is quickly expanding (and a significant part of my dissertation).

tl;dr: In the ancient world, literacy rates were very low and literacy was acquired with a distinctively oral-performative emphasis--i.e., reading aloud to other people. Silent reading was not really the point of ancient scribal training.

On literacy in Iron Age Israel please see: C. A. Rollston, Writing and Literacy in the World of Ancient Israel--this book is very accessible and very important as far as the implications of Rollston's conclusions are concerned. Definitely check it out.

David Carr's Writing on the Tablet of the Heart deals with this topic as it pertains to scribal education/literacy education in ancient Egypt, Mesopotamia, Greece, and the Levant (i.e., Israel, Judah, etc.). He specifically notes that scribes/literati were not trained for silent reading; but, rather, that they were trained as part of an oral literacy program, whereby scribes were trained to read things aloud to an audience--whether it be through performance, or a letter, etc. Some primary data Carr points out:

One early manuscript for the Hebrew prophets does not even record the complete words of each verse. Instead, only the fist word is given, along with the first letter of each succeeding word...written copies were a subsidiary part of a much broader literate matrix, where the focus was as much or more on the transmission of texts from mind to mind as on transmission of texts in written form. Both writing and oral performance fed into the process of indoctrination/education/enculturation. (p. 5)

Carr's definition of 'literacy':

...the literacy that most counted in these ancient societies often was not a basic ability to read and write. Rather it was an oral-written mastery of a body of texts. Moreover, this 'literacy' was something that separated the members of an elite from their contemporaries. (p. 13)

We might readily think of things like the Babylonian Akitu festival, where epic-narrative texts that detailed Babylonian creation myths were told and re-told out loud (alongside the existence of written copies, which were likely strictly for the training of new generations of scribes). That is to say, the written copies were used as training texts for new scribes so they could function in various social roles, oftentimes cultic and performative in nature.

We might also cite Karel Van der Toorn's book Scribal Culture and the Making of the Hebrew Bible, where he notes that literacy rates in the ancient Near East were incredibly low and that,

writing was mostly used to support an oral performance. The native verbs for 'reading' literally mean 'to cry, to speak out loud' (Hebrew qārāʾ, Akkadian šasû and its by-form šitassû). (p. 12)

A big part of KVdT's first chapter is highlighting the fact that "books" are a relatively late idea--even in the sense of biblical books. Significant portions of biblical texts are actually compilations rather than formal books--we can think of things like Psalms and Proverbs (and even many prophetic texts).

So, yeah--silent reading wasn't really a thing in literacy's earliest stages. It's not something that really picked up until later. (Which others can certainly comment on better than I can.)

Question: Wouldn't the existence of writing, such as cunieform tablets, oracle bone inscriptions, and hieroglyphs, demonstrate an ability to read silently? How would carvers and scribes sound out partially completed non-phonetic words?