There's no one answer to this question. While Rabbinic texts contain historical discussion, there's no particular timeline that's authoritative. They fundementally aren't in the business of telling over a historical narrative, even if they sometimes do. Further, there's no hard point where they "converge".

There are specific events you can look at. The Hasmonean Revolt is a good example of why this question is difficult. The Hasmonean Revolt is an event historians (to my knowledge) assumed really happened. And it is referenced in Jewish sources. But, historians believe it mostly because it's in Jewish texts, namely Josephus and the Books of Maccabees (and because it fits with other events in the region). But those texts aren't really part of mainstream Rabbinic tradition. Rabbinic texts do mention things like a miracle occuring with oil when the Temple was reconquered, which historians would be skeptical of. Would we call that convergence, or not?

Before that, we can have the same conversation about narratives in the bible. Depending on the historian, most would probably agree that some of the Israelian Judean kings in the bible were real, they probably were from a Davidic dynasty, and maybe some of the wars and characters mentioned were real. For some of these, it's speculative, because the only source is the bible and it's a gamble how much of the bible is assumed to be historically accurate for what isn't attested elsewhere. And it's fairly clear that the bible has a particular religious agenda in describing the events. It's hard to call that "convergence", but it's also hard to not call it convergence.

And on the later end, you could take an event like the destruction of the Temple in Jerusalem. It's reference in Rabbinic texts, Roman texts, and can be verified archeologically. But it's not certain if the description in Rabbinic texts is authentic--things like dates, characters, details of the war, etc. It's not like history text anthologized from Rabbinic texts would match perfectly with a secular history.

So, it depends on what you mean. The first events that an academic historian and someone who's only read Rabbinic texts would agree on would probably involve the Judean and Israelian kings, but there's no hard point you could state, and they wouldn't agree on everything from there on. And that's ignoring systematic issues like the [missing years in the traditional Jewish year-dating system](https://en.wikipedia.org/wiki/Missing_years_(Jewish_calendar)).