I hate to say this, but I'm afraid you are all mired in the fuzziest of thinking here. Each of us, at the moment of birth, automatically becomes a member of the next generation, as far as our parents are concerned. So, if you were born of woman, and didn't spring straight from the belly of one of the Titans, then you are a member of somebody's "next generation". By the amount of navel-gazing (or omphaloskepsis, if you prefer) that goes on around Wordie, we can be confident that everyone has a navel. So we are all part of the 'next generation', just as it's always cocktail hour somewhere on earth.
From a linguistic perspective, this apparent 'difficulty' is a result of the non-absolute nature of the term 'next', perhaps compounded by the non-specific nature of the word 'generation'.
If you would like an alternate resolution of your paradox, invoking the oddities of time travel and the equivalence of the space-time continuum, it will cost extra.