Why did early Christians think that Jesus was conceived and died on the same time?
There is no scriptural basis for this that I know of, it is possibly oral tradition. In keeping with Hebrew festivals, which or not on a Gregorian calendar but follow the lunar cycles, the exact date of Christmas is probably Hannukah! (Just my thought)
Having the same birthday and day of passing is a Jewish sign of having “come into one’s days” ie, a perfect life(span.) For instance, Moses, in Jewish tradition, was born and passed on on the 7th of the month of Adar the month before Passover.
Therefor, as appears to the Jew, this seems to be the grafting of Moses’ (Jewish) perfection (l’havdil elef havdalos) onto Jesus. The early Jewish Torah-true Jesus-as-messiah cultists would have known this.