In neither situation does「才」mean talent - it is quite easy to make a parsing mistake, especially in the first question referring to「才能」.
「才」is widely used as a phonetic loan (that is, not related to the meaning talent) in Modern Chinese meaning only; only then. This is why you may see alternative representations in some other texts, such as「纔」, which I'll use here.
Many children think that, only after they grow up, they have the freedom to do as they wish.
The meaning is not comparable with「纔」omitted. In this situation, if「纔」is omitted native speakers will treat it as if「就」is omitted.
Many children think that they can have the freedom to do as they wish as soon as they grow up.
In the second question,「纔」similarly means only, and is used for emphasis.
Little do they know, only they are the ones with the freedom.
The emphasis is on only the children having the freedom, and not anyone else.
Since「才」(talent) is a noun, to avoid parsing「才」incorrectly, recognise that talent/talented is something that people have or are:
Without「有」or「是」occurring before「才」, you're most likely looking at a meaning not related to talent. Of course,「剛才/剛纔」(just a moment ago) has nothing to do with talent either.