Don't gum up your logistics on their account; I didn't ask because I wanted help patronizing them.
Back in Valinor it was a real and intractable political problem that you needed a hundred years' experience at anything to be good enough at it that it was faster for the really good people to tell you what they needed than for them to just do it themselves. We no longer have the problem to the same degree, here, but if I had a solution to the expertise gap in my pocket I'd have used it long ago.
And two hours later someone arrives at a run along the rooftops and drops a letter at her door that contains a description of things Men could do with their time, how much supervision or what resources he expects it to require, and how those resources would otherwise be deployed. In no cases except cleaning the streets and the palace would the Men be producing something more valuable than the resources (counting Elf time) used, though he doesn't draw attention to this.
And then she gathers some interested Men and explains that the city was designed to be run entirely by Elves, all of whom have known each other a really long time and don't need as much rest as she/Men do and have not for the most part picked up the Men's language. Any work done in groups is going to be hard to fold Men into, especially since they probably aren't going to stay long by slow Elf standards. The only thing Maitimo could come up with that wouldn't have this problem is cleaning. Everybody likes having clean streets and somebody's gotta do it, but this is not the variety of options she was hoping to have to offer.
They could focus on being useful to each other - babysitting each other's children, making sure there's no conflict escalation when people get into fights, making clothes that suit their own styles better than whatever the Elves have lying around - and she's going to try to think of other things they can do without requiring Elf attention or cooperation and maybe they can think of things too. She might ask some Dwarves for advice too because Dwarves think a lot about problems to do with how to make sure sources of value aren't just sort of sitting around.
Meanwhile, anybody want to study Quenya? It was never very useful when there were only twenty Elves around, but now there's loads.
Okay! She doesn't speak it herself, but here's the alphabet, and the reverse of the phrasebook she gave Maitimo, and their versions of numerals because the Men have been using the Doriath ones, and their Elf friends will surely be happy to help.
Do they have any ideas about the skill gap problem themselves?
Making Men useful to Elves isn't really a good goal anyway, and it's ridiculous if the Feanorians are trying to hold the Men to that standard. Childhood is a time for learning and exploring, not creating more value than you consume. Has she considered that Maitimo is not a very honest or trustworthy person and probably has ulterior motives?
She's not sure his trustworthiness is at issue here at all, and the point isn't to make them useful to Elves per se, it's to make them useful to the city they're living in because except for the ones who are yea high they are not actually children and will not be perpetually comfortable as dependents.
That last has a language barrier problem. Loki knows how to make bows and arrows, though. She goes and finds the nearest Elven archer to see if there's anything about the bow design that would make the kind she knows incorrect for the local style.
Cool. She'll just go gather up an armful of sticks and whatnot from the wilderness and pop them back and teach some Men to make bows and arrows to the point where they can teach others. Target practice is to be approached very cautiously, please, she doesn't want to have to come deal with somebody's arrow wound.
She works a bit and then she does go ask Dwarves for advice. (And to see if they want to let her accumulate a bankroll with quick courier and small cargo transport work.)
The Elves may or may not have heard of comparative advantage! She considered explaining it but it seemed like a transaction cost problem to her as much as anything.
Just like Elves to build institutions with ridiculously high barriers to entry and then end up wasting a significant part of their labor force. Can Men copy books? Copying books should be about as time consuming for a Man as an Elf, and doesn't require much expertise. If Men's books are sloppier and sell for less there'd probably still be a buyer.
Ooh, that's a great idea, Men scribes. Some of them are learning the Quenya alphabet anyway already!