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This turned out to be weirdly hard to look up online, so I cracked my copy of the book open to settle the question.

EARLIER Ravens

Egwene's youngest older sister Loise is 15. It takes Egwene two years to be allowed to do the same shearing day chores, and she gets to do them a year early, so she's no more than 12 in the prologue. I remember her being 11, but without reading more closely, I don't recall why exactly.
The boys are a couple of years older than Egwene, making them no more than 14.
Nynaeve is pretty clearly stated to be 17 (a year younger than another girl who's 18).

Chapter 1

Rand and Mat are years older than Ewin, who's 14. So, they are at least 16. They're dismissive of him based on his age, which they aren't towards Egwene, so presumably Egwene is at least 15.

Chapter 3

Mat is old enough to be married.
Nynaeve is "not all that much older" than the boys.

Conclusion

Ok, it's hard to sort back through, without taking the time to reread in detail.
I don't recall how much time passes between Ravens and Chapter 1, but I do recall there being a conversation between Moraine and Egwene where it's mentioned. I remember it as being five years earlier, which doesn't greatly clarify anything.
I also recall, from maybe the third book, that Rand is stated to be 20 and that they've been away from home for more than a year.
Also, I don't ever recall Egwene being said to be unusually old to go to the White Tower and they don't usually accept novices over 18.
My sense is that Egwene is about 16 in Chapter 1, while the boys are 18. That's a little bit older than I remember being the case.
The fandom timelines do more closely match yours, though, and the 20 years since hearing the prophecy does ring a bell.
Keep an eye out for details that will paint a clearer picture as you continue reading. I'll be curious to know the answer.
You get extra sats for cracking open the book.
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Thank you, sir.
I had a clear impression of their ages when I first read it, but the information is presented in a maze of relative statements about who is older than who and at what age different customs take effect.
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I just read both the prequel and the first one. So it’s still fresh in my mind. I remember, in the prequel, Moiraine and Siaun are there for the foretelling 20 years prior the first book. The foretelling says the dragon reborn is now on earth or something and from then on both of them vow to find him. It is stated that mat Perrin and Rand are about the same age so they are 19 at most on the first book and by the second they are twenty 20. Not only are they ta veren and that the blood of manetheren is strong but also Moiraine knows the prophecy and so does Lan so they both know it has to be one of the three since they match the age according to it. They seem young to me but never as young as teenagers. Maybe Egwene but I don’t remember anything about her age. Both her and the wisdom are going to become novices despite their ages because they are that strong. Despite Nynaeve being older than usual and egwene being so young. I just read it in the great hunt one of the aes sedai makes a comment on both their ages. They are different and strong. Oh my hahaha what a debate on their age. 👵
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Apparently, they were all intended to be older, but Robert Jordan rewrote them to be younger because that matched the age of expected readers better.
There are several mentions of Egwene being two years younger than the boys, so pinning anyone's age down should tell us how old everyone else is.
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By going with the books In the eye of the world the boys are around 19 and egwene around 17 👵👴
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