I'd suggest X/Y.
It's an easier game to beat, so even a team of baby Pokémon should be able to fight through it. If you have access to a second console and another compatible game, you can prepare the team you want on a different game, and then trade to the one you're attempting, this way the Pokémon you want are there pretty much from the get go. If you are limited to a single console, you can use Pokémon Bank and pull them out of the earliest available Pokémon Centre (depending on the game, there are other variables that may need to be met). Gen 5 and earlier, you would need a second console for this. You would also miss out on the broken EXP share that would give your adorable team a much needed level boost without copious grinding.
I imagine it may be difficult, if at all possible, to assemble a full team of baby Pokémon within the progression of a single game. There are 18? of them, and I don't know if any games would have 6 of them readily available in their unevolved state.