Babies are actually pretty bad at learning language. It's just that it's the only thing they have to do. Adults are much better at learning language, but they never put any time into it.
As an adult, if you were sent to an immersion program in a foreign country with two full-time foreign tutors/caretakers who loved you, like legitimately loved you with all their hearts, you would pick up that new language pretty darn quick.
The advantage is that it's easier, and often more pleasant, to integrate.
That said, babies do have some neuroplasticity advantages.
We should play to our strengths - babies are hopeless at grammar drills, and adults aren't as good as babies at neuroplasticity - by applying our brain to the problem.
I say that, while having built a comprehensible input tool (https://nuenki.app). But it's useful as a complement to that study, as you can more readily run a browser extension or listen to podcasts than devote your entire life to focused study.
There are different levels of fluency that language training professionals recognize, mostly standardized on the ILR scale [0].
There are 5 levels on this scale. What people commonly consider "fluent" is level 3. There are also midpoints recognized by a "+", e.g. most people who study language seriously but don't have any special aptitude for language training get to a 2+. It's an open question of serious debate and active research of whether it's possible to train anyone past 2+ to 3. Some rare individuals seem to have an innate aptitude for language acquisition and they seem to breeze through their training to 3 and then continue on from there. Everyone else seems to plateau at 2+.
3 is just the level of "can easily be understood as a foreigner by a native speaker". It's not native level of mastery. "So fluent you can fool a native speaker" is 5.
All of that is to say that children are most definitely not fluent by the time they reach school age. Most children starting school will be at a 0+ level. Particularly intelligent children might be at a 1. But they are definitely nowhere near 3.
And indeed, by the time most people graduate highschool, I would struggle to admit that they are much beyond 3. Hell, I'd even say a large portion of people graduating college don't have mastery of their native language.
So no, I don't think children have a particularly large advantage in learning language. Despite significant, continue training in language for the first 18 years of their lives, most aren't able to get very far beyond what any studious adult can learn in 2 years.
[0] https://en.m.wikipedia.org/wiki/ILR_scale#ILR_scale
Edits: damn glass keyboards making my own fluency look suspect
You might be thinking to apply measurements meant to verify a grown-ups fluency (with all that that implies: vocabulary, idioms, ability to detect nuance, etc.) for children, which is in my opinion a flawed methodology.
"Fluency" is when you can easily speak without having to construct the sentence in your mind, not even for a moment. It just comes out. It _flows_, which is what the term originally meant. Being fluent does not imply that you can talk about anything and everything from philosophy to Bach, or whatever.
To hear "It is extremely rare for any child to be fluent in any language by the time they start school".. that makes no sense. Of course every single child is fluent in _at least_ their native language when they reach school! And long before.
Some are fluent in more than one language, but it's much rarer. Though I do know a family where all three children were fluent in three languages before they started school. Special circumstances though, and thoroughly anecdotal.