I found the quote you're talking about, which the internet gives as:

The beginning and ending of Ezekiel, the third of the four, are involved in so great obscurity that like the commencement of Genesis they are not studied by the Hebrews until they are thirty years old.

Which is more specific, but also accords better with Jewish sources. The beginning of Ezekiel is associated with "ma'ase merkava" in Jewish sources ("works of the chariot" I guess is the best way to translate this), and the beginning of Genesis with "ma'ase bereshit" ("works of creation/genesis"). These are two types of Jewish mysticism which are referenced in the Talmud, which presumably are some sort of proto-kabbalah (which is Jewish mysticism as a whole, most of which is written about in the late Middle Ages.

The Talmud (which is a compilation of source material roughly equivalent in time with Jerome) doesn’t say all that much about what those two sorts of mystical teachings are, but it does seem to think of those teachings as being powerful, but also dangerous to teach to the unlearnèd. The Jewish texts therefore records rules about who can be taught these topics, and in what context. The Mishna (2nd century law code) records:

אין דורשין בעריות בשלשה ולא במעשה בראשית בשנים ולא במרכבה ביחיד אלא אם כן היה חכם ומבין מדעתו

One does not expound on forbidden sexuality before three, nor ma’ase bereshit before two, nor “the chariot” alone unless one is wise and understands it on his own

Which seems to imply that ma’ase bereshit mustn’t be taught publicly, and ma’ase Merkava should not be learned in general by regular people. It’s clear from the Talmud that these are understood as limits on how many people these can be taught to, not maximums, if that wasn’t clear from context. The Mishna continues that people who delve too deeply into certain philosophies, it would better had they not been born.

The Talmud then begins a discourse on this subject, both talking about the importance of not revealing these mystical topics, the qualifications needed to study it (which include expertise in a wide variety of subjects, including bible and astronomy. Someone can be “not old enough”, but no specific minimum age is given), and then has some discussion of the topics it says not to talk about. In another passage about esoteric teachings, one of the requirements is to be at “half your lifespan”, which isn’t a specific number, but gives you a ballpark.

Much later than Jerome and the Talmud, in the Middle Ages, people start putting hard ages on this. There are references to achieving wisdom at forty, which becomes the most commonly cited minimum age. Other ages pop up too, such as thirty-five and fifty, but forty is the most common, and in the early modern period was sometimes issued as a definitive rule (though not always applying to all mysticism). It doesn’t seem there’s ever been a universal Jewish age-limit, but there’s a consistent theme of limiting dissemination of mystical teachings to those who already are well-versed in more mainstream Jewish texts. And to ensure that and the required maturity age limits have existed, but not as early as Jerome. This site goes through a wide variety of sources on this, without giving a reference to thirty years old.

So there’s no hard documentary evidence for any hard age limit as early as Jerome, and no evidence for thirty. However, Jewish texts are not a complete description of what was going on in Jewish communities. We know these teachings were considered esoteric, so it’s not outside the realm of believeability that there really was a community Jerome was aware of that required people to not study these topics before age 30—it even (roughly) fits with the “half of lifespan” reference, though that reference isn’t about either Chariot or Creation mysticism (it’s about naming God).

However, there’s much less evidence that these actually led to restricting reading the biblical text. The Mishna above is specific to expounding the text. Knowledge of the bible in general was considered basic religious knowledge. Certainly the beginning of Genesis would’ve been familiar to people, just as the passages about forbidden sexual relationships are, both from a religious education and from public liturgical reading. While such an education wouldn’t’ve been available to every person, getting your hands on the text, or hearing it, would not have been more difficult than any other part of the bible. There’s a passage in the Mishna which lists pasts of the Torah which are read publicly but not translated, and Genesis 1 is not among them. There’s a reference in the Tosefta (another ancient Jewish text) specifically saying that one may read and translate Genesis, which the Talmud understands to mean that even though uninitiated listeners might start to ponder mystical teachings, the passage is read and translated nonetheless.

With the “chariot” passage, it’s a bit more complicated. The Mishna records an opinion Ezekiel 1 mustn’t be read in the prophetic lectionary, while also recording an opinion disputing that. The Talmud does list it as the prophetic lectionary choice for the holiday of Shavu’ot, which means that it would’ve been widely heard, so the consensus presumably follows the latter by the time the Talmud was compiled, but not in the time of the Mishna. Jerome would’ve fit right in that time gap. But Jerome seems to be talking about private reading, with public reading definitely not taking place (if a text is read publicly, banning those under 30 from reading it won’t do much good if they show up to services). While not reading Ezekiel 1 makes more sense than not reading Genesis because there are recorded opinions banning it from being read publicly, there’s also no evidence of banning it from being read privately under 30. One would assume the opposite, since educated children in the Talmud usually are depicted as learning the Prophets. But, in Jerome’s time it’s possible the local practice was not to read Ezekiel 1 publicly, and not to expound on its teachings to those under a certain age.

The end of Ezekiel is a vision of the Temple. I am unaware of any scritures around teaching/reading that whatsoever. It’s possible it existed, but there’s no evidence for it to my knowledge.

But, the quote I found from Jerome specifies study. I can't read Greek Latin, so I don't know what wording Jerome used. If he did mean "study" in the sense of "hear teachings from", not the sense of "read the verses", then the basic premise would accord with what we know of limits of Jewish mysticism quite well. The only pieces that are somewhat suspect are a hard age restriction (which sometimes existed in Judaism, but later) and inclusion of the end of Ezekiel (which I am unaware of whatsoever).