You are making the claim that no such writings ever existed for other cultures to make the differentiation but the way I see it that differentiation cant be established.
Why not? Have you studied mythic literature? The whole reason behind differentiation is that it is based on "differences." What myth can you point to that describes its founder as having lived merely decades prior to the foundation of the cult? What mythic "godman" can you point to who had disiples mentioned by contemporaries? There are none. Certainly there are wonder and miracle workers other than Jesus who are written, but they are historical figures, not myths (for example, Apollonius of Tyana is probably historical, although we have less information about him that for Jesus).
Your problem is that you are rejecting these texts as entirely mythical because they contain myth. However, analysis of greco-roman literature places the gospels into the genre of bioi/vitae (as I am getting tired of saying). In other words, they are biographies of sorts, not myths. Most of ancient history contained mythic elements. By your argument, we would have to reject virtually every single historical text. Why not, instead, parse these text, reject the miraculous, and try to determine historicity? Experts have been doing this to the gospels for centuries, and as a result their is unanimity among experts that the gospels contain a historical core and that Jesus was a historical figure.
Even if I granted that such a differentiation could be made I still dont see your logic
It's quite simple. I'll explain via steps if that helps.
Basic Steps in Determining historicity:
1. The genre of the text: If the text is not interested in recording history (say, because it is a play, or a novel) than a priori it is far less likely to be historical. The Gospels are bioi/vitae, and so are concerned with historicity. This does not mean they would count as history by today's standards, but then neither would most (perhaps all) of ancient history. All of it, from Herodotus to Pliny to Plutarch, has to be analyzed and parsed to determine historicity.
2. Date: How far removed is the text from the events described? For most cults, their foundation myth is based on events which happened eons ago, not within living memory as with our earliest references to Jesus
3. Multiple attestation: We have many independent references from various sources attesting to Jesus' existence. Within a generation of his death (i.e. while people who were living during Jesus' mission) we have Paul, Q, Ur-mark, Hebrews, and Mark. That is an enormous amount of information compared with most historical figures referenced in ancient history.
4. Reliability of sources: The gospels are based on oral tradition. As such, they are only as reliable as the transmission of this tradition. Examination of orality within similar oral cultures, oral cultures in general, extra-canonical evidence, and within the NT texts themselves reveals that the transmissions of the Jesus tradition was controlled. In otherwords, the bulk of his teachings has likely been reproduced fairly reliably. Certain narratives are also likely to have been transmitted accurately. Where no information was available in the tradition, it appears that (as with other oral traditions) innovation occured (for example, the birth narratives).
In short, when it comes to the existence of Jesus, we have more evidence than for all but a handful of ancient figures. To suppose he is entirely mythical is ridiculous given the date and genre of the sources.
I would suggest you read any number of scholarly works on the historical Jesus.
I don't remember Paul or Mark or anyone for that matter giving a "date" of Jesus' death or birth
So what? Matthew and Luke give his birth as occuring during Herod's reign. However, even if we reject the birth narratives as wholly ahistorical, there are still numerous dates for his life which can nail down the time of his mission (and therefore give a time period in which he lived that is close to the time of literary reference, unlike myths). The passion narrative predates Mark, and records Caiaphas as the high priest. Caiaphas is attested to elsewhere, lending credence not only to the narrative itself but also giving an approximate date of trial. The same is true of Pontius Pilate.
Likewise, John the Baptist and Jesus are recorded in multiple independent traditions as having been contemporaries, again giving a date for Jesus' life (as John the Baptist is also independently attested to).
We also know roughly when Paul lived, and he knew Jesus' disciples, again helping with dating.
In short, we don't need exact dates in order to be historically certain that Jesus lived during a particular period.