A second hand guitar also is NOT a bad thing, sure it might need new strings, or even fret dressing/setup (which costs about £50 at any good guitar shop), but the wood "breaks in", and the tone of a guitar actually improves over time. Actually, I'd go as far to say that a poor guitar will never sound great and probably get much worse (fret buzz etc, unplayable notes, twisted neck etc), whereas a good guitar will carry on sounding good. If it's been knocking about a bit, and it still sounds good, well there you go, there's most of your test of quality as to how it's been made. Because wood literally moves and changes shape very subtlety over time. A well constructed guitar won't have problems like this.
I have picked up random guitars in flea markets, I know most all the brands, the cheap Spanish/Mexican ones, the ones that are made in China (not always bad at all), Japan, places I've never heard of before or just Europe generally. Some of them can be made to sound fantastic, but that has to be some credit to me, to be fair. I know how to get the most out of an average sounding guitar. But I know when I pick one up, what's a "good" guitar and what is, well, a dust trap. The dust trap ones probably retail for under £100. They have cheap lacquers and dull looking wood. But that's not to say a dirty guitar can't clean up very well!
You might have a £300 guitar kicking about that's simply forgotten and depreciated, or just one that happens to have come from a shop far away somewhere where there were real craftspeople, employed to make them. Have a real good look at the guitar. If it looks cheap, it is cheap. There should be visible grain in the wood, the parts should be close fitting with no gaps at all, there should literally be colour and depth to it, as well as in the sound. If it looks dull, ask if you can rub some oil into it. Any natural oil will do. The wood should glisten. Indeed, the guitars you find knocking around that don't that that horrible cheap lacquer slapped on (I mean this can be done well, but still), those were probably French polished once, and can have a much better tone. Those things aren't a coincidence - it's an integral part of the guitar that it's contructed in such a way, with care, and of certain woods that it will resonate well. Perhaps surprisingly, although perhaps less important, the same is true for any electric guitar (but that brings in the subject of multi part construction, truss rods, pick-up mounting, bridges/tremolos and pick up types which is a whole other story. You have less of this to think about with an acoustic because it is ultimately all glued together to form one single part. Most people can assess with a reasonable degree of scrutiny when comparing acoustic guitars, which one is probably better than the other. But it's much much harder to do that with an electric guitar because so much depends on the amplifier as well).
If your kid complains that acoustic guitars are not cool. Just show them some of their favourite musicians playing acoustic guitars. Show them some amazing blues/jazz music on YouTube. A lot of classic rock and pop songs were written on acoustic guitars. You can play them as hard or as soft as you like and get a huge range of tones.
And since it's a "lad", perhaps mention that some decent melodic guitar music goes down VERY well in certain social settings. You might get a lot more than your bargained for investing time in musicianship than whatever your first guitar cost
Hell you can probably find a wife learning the 3 chords in Wonderwall, even if I refuse to play it.