According to the Bible, the Israelite history of the city began in c. 1000 BCE, with King David's sack of Jerusalem, following which Jerusalem became the City of David and capital of the United Kingdom of Israel. According to the Books of Samuel, the Jebusites managed to resist attempts by the Israelites to capture the city, and by the time of King David were mocking such attempts, claiming that even the blind and lame could defeat the Israelite army. Nevertheless, the masoretic text for the Books of Samuel states that David managed to capture the city by stealth, sending his forces through a ``water shaft ''and attacking the city from the inside. Archaeologists now view this as implausible as the Gihon spring -- the only known location from which water shafts lead into the city -- is now known to have been heavily defended (and hence an attack via this route would have been obvious rather than secretive). The older Septuagint text, however, suggests that rather than by a water shaft, David's forces defeated the Jebusites by using daggers rather than through the water tunnels coming through the Gihon spring. There was another king in Jerusalem, Araunah, during, and possibly before, David's control of the city, according to the biblical narrative, who was probably the Jebusite king of Jerusalem. The city, which at that point stood upon the Ophel, was, according to the biblical account, expanded to the south, and declared by David to be the capital city of the Kingdom of Israel. David also, according to the Books of Samuel, constructed an altar at the location of a threshing floor he had purchased from Araunah; a portion of biblical scholars view this as an attempt by the narrative's author to give an Israelite foundation to a pre-existing sanctuary.
The Apostolic sees claim to have been founded by one or more of the apostles of Jesus, who are said to have dispersed from Jerusalem sometime after the crucifixion of Jesus, c. 26 -- 36, perhaps following the Great Commission. Early Christians gathered in small private homes, known as house churches, but a city's whole Christian community would also be called a church -- the Greek noun ἐκκλησία literally means assembly, gathering, or congregation but is translated as church in most English translations of the New Testament.
Vasilopita (, "Vasilópita", lit. '(St.) Basil-pie' or 'king pie', see below) is a New Year's Day bread or cake in Greece and many other areas in eastern Europe and the Balkans which contains a hidden coin or trinket which gives good luck to the receiver, like the Western European king cake. It is associated with Saint Basil's day, January 1, in most of Greece, but in some regions, the traditions surrounding a cake with a hidden coin are attached to Epiphany or to Christmas. It is made of a variety of dough, depending on regional and family tradition, including tsoureki. In some families, instead of dough, it is made from a custard base called galatopita (literally milk-pita). The pie is also known as Chronópita (Χρονόπιτα  χρόνος: "chrónos ⇨ time/year" + πίτα: "píta ⇨ pie"), meaning New Year's Pie.

Question: When did the city that spread Christianity to Rome, Egypt, Judea, and the country where Vasilopita originates, become the capital city of the Hebrews?
Answer: c. 1000 BCE