Our insatiable appetites for information, stimulation, validation will come with us. But when all those wants are met no sooner than they have been felt, the knowledge of what it is to be left unfulfilled may not.
So, this sentence is not very well-written; I don't blame you for being confused by it.
- the noun "want" normally means a deficiency or a lack; but in this case it means a desire.
- the sense of "wants are met no sooner than they have been felt" is backward; the author meant to write, "wants are no sooner felt than met", or "wants are met as soon as they are felt".
- the "may not" at the end is elliptical for "may not come with us". This would be fine, except that the sentence is pretty long and complicated, so there's too much between the "may not" and the original verb phrase that is here being elided.
- the phrasing is appropriate for a warning about the downsides of technological advance, but then it doesn't make any sort of case for why we would want to retain the knowledge of what it's like to be unfulfilled. I'm actually still not sure whether the author views it as a good thing (and chose poor phrasing) or as a bad thing (and argued it poorly). I can only hope that it's clearer in context.
The overall intended meaning of this sentence is, "When our desires for information, stimulation, validation are all instantly satisfied, we will no longer know what it's like to be unfulfilled."
Only by doing this can the last generation to know a pre-internet world ensure that those who come after appreciate what has been lost.
Is 'to know' a predicate? Where is the subject after aux verb 'can'? Where is the subject of predicate 'ensure'?
"To know" by itself is not a predicate, since it has a direct object, namely "a pre-internet world". The whole phrase "to know a pre-internet world" is a modifier in the larger phrase "the last generation to know a pre-internet world", meaning "the last generation that knew a pre-internet world".
"The last generation to know a pre-internet world" is also the answer to your other questions: it's the subject of "can […] ensure that those who come after appreciate what has been lost".