We already know of instances of societal-cultural upheaval or even trauma, so severe, that the language undergoes unrecognizable transformation in the form of pidgins. A group of young people from scattered tribes after some disaster, who speak no common language, and who are barely lingual and "re-invent language" for the next generation, seems quite possible over the last several tens of thousands of years, perhaps in multiple times and places.

The similarity of grammar, in unrelated creoles, descended from such pidgin languages, is one of those great tantalizing mysteries in linguistics, and in my view, one that suggests we might just be wired to make a language if we didn't already have one, as do things like the apparent spontaneous emergence of sign languages in deaf communities. The spanner in the workers for that theory is that, of course, those hypothesized people who didn't speak related languages still grew up in lingual communities and were exposed to the idea of language from birth (even the deaf ones, really). Perhaps such events are just a remixing of what already was culturally common, and common to all humans. Indeed, perhaps no community where the link of language transmission has been completely broken, could even survive.

Isn't this Chomsky's thesis about humans having an ingrained "grammar" (or proto-grammar, or grammar machinery) from birth?

I wonder though how do reconstructed/revived languages such as modern Hebrew fit into this picture.

Latin is clearly distinct from English, even though both languages share a common ancestor and English itself was heavily influenced by Latin, both directly and indirectly. Yet it is still useful to make the distinction between them as separate languages and what we call Latin is clearly older than what we call English.

I don’t think it’s at all useful to say Latin and English are the really the same age, even if it’s technically true per your definition.

Latin is of course clearly older than (Modern) English, because it was spoken 2,000 years ago, whereas English is spoken today. But Mediaeval Latin was spoken at the same time as Old English; while Latin turned into Spanish, French, Italian, Romanian etc., Old English turned into Modern English.

Arguably, these are just quirks of nomenclature. It's just an accident of history that Old English and Modern English are both called "English", because the difference between Old English and Modern English is just as great (if not greater) as the difference between Latin and Spanish.

The verbal paradigm in Spanish for example retains far more similarities to Latin verb conjugation than is the case with Old and Modern English.

No. That makes Latin younger than modern English, not older.

Of course languages known to us only from a certain time period are associated with that time period. They're a snapshot of that linguistic tradition. Living language traditions don't really permit comparisons of age, because they exist in the present.