When did the Israelites possess the Promised Land?

Answer 1

The Patriarchs and their family were in Israel (Canaan) for 220 years. The era from Joshua until the First Destruction (including the Judges and Kings) was 850 years. The Second Temple era was, according to traditional chronology, another 420 years (not 586), which included the Hasmonean dynasty. That's a total of 1490 years. (See: Jewish history timeline)
After the Second Destruction, there were thousands of Jews who remained in Israel (Judea; Palestine) throughout the Talmudic era and beyond (see for example the Talmud, Sanhedrin 17b). They were the majority of Palestine's population well into the fourth century, with records attesting to at least 43 Jewish communities, most of them in the Galilee and Jordan valley. After that, there were still Yeshivas in Israel with at least some thousands of community-members.

In the fifth century, the Jerusalem Talmud was redacted in the yeshiva of Tiberias, by the disciples of Rabbi Johanan; and the Christians of Palestine declared the Jews to be a tolerated minority.
In the sixth century CE, Mar Zutra and his descendants served as head of the community and the Rabbinical academy in Tiberias.
In the seventh century, the Palestinian Jews joined the Persians in a battle to take Jerusalem from the local Byzantines, and enjoyed a brief autonomy, which the Byzantines under Heraclius officially recognized in 628.

At the time of the Moslem conquest of Palestine in 638, the Jewish population in the land has been put at no less than 300,000; and a period of flourishing began. Caliph Umar encouraged Jews to resettle Jerusalem.
In the eighth century, there were 30 synagogues in Tiberias. A Jew named Abu Issa brought his forces in battle against the Caliph.
In the ninth century, the Jews of Palestine instituted their own Gaon (leading sage) in Tiberias and later in Jerusalem.
In the tenth century, we have the greatest of the Massoretes, Rabbis Aharon ben Asher and Ben Naphtali, flourishing in Tiberias.

Contemporary with Rashi (11th century), we have a Rabbi Abiathar and others, who lived in Israel (see for example Rashi commentary, Talmud Berakhot 62a), and large Jewish communities in Rafah and Ramle, Hebron, Acre, Caesaria, Jaffa, Ashkelon and Gaza.
In the 12th-13th centuries, the Palestinian Jews were harshly persecuted under the Christian Crusaders, yet many Jews continued to live in all the above-mentioned towns as well as Haifa, with Judah Halevi journeying to Palestine in 1141, Maimonides in 1165, and Nachmanides in 1286.

In 1187, Saladdin invited more Jews to settle Palestine. In 1204, a group of Maghreb Jews arrived; and in 1211, 300 Rabbis arrived from France and England. In 1260, Rabbi Yechiel of Paris established a Talmud academy in Acre.

Since that time, the continual presence of Jewish communities in Palestine (Israel) is well-known and needs no reiteration.

A brief timeline of Israel and the Jews:
1) c.1950 BCE: Noah delegated what is now called Israel to the Semites (children of Shem) (Rashi commentary to Genesis 12:6).
2) c. 1750 BCE: The neighboring Canaanites gradually take control of the land (ibid) which therefore becomes called Canaan.
3) 1737-1522 BCE: Abraham, Isaac and Jacob spread their teachings in the land. God promises this land to them and their descendants (Genesis ch.28).
4) 1272 BCE: The Israelites under Joshua, at God's command, enter the land (Joshua ch.3-4) which now becomes called the Land of Israel. They remain for 850 years.
5) 422 BCE: The Babylonians destroy the First Temple, exiling the Jews.
6) 352 BCE: The Persians permit the Jews to rebuild the Temple. Tens of thousands of Jews resettle in Israel, now called Judea, while others remain in Babylonia.
7) 68 CE: The Romans destroy the Second Temple. Most of the Jews in Judea slowly scatter afield, but some thousands remain. Judea is renamed Syria-Palaestina by the Romans.
8) 1096-1270: the Crusades.
9) from 1492: after the Spaniards expel all Jews from Spain, thousands relocate to the Jewish communities in Palestine.
10) c.1780-1880: The first wave of Aliyah, mostly religious Jews, who move from Europe to Israel (Palestine) in the thousands.
11) c.1880 onward: the large-scale Jewish return to Israel gets underway.

See also:

Is Israel still protected by God?

Answer 2

The Jews got into the promise land after the death of Moses. Thirty-nine years after Moses received the law Joshua lead them into the promise land. Moses died right before that (1240 B.C).