The Exodus from Egypt
Thus the children of Israel were liberated from the yoke of their oppressors on the fifteenth day of Nissan in the year 2448 after the creation of the world.
There were 600,000 men over 20 years of age, with their wives and children, and flocks, crossing the border of Egypt that day a free nation. Many Egyptians and other non-Israelites joined the triumphant children of Israel, hoping to share their glorious future.
The children of Israel did not leave Egypt destitute. In addition to their own possessions, the terrified Egyptians had bestowed upon them gifts of gold and silver, and clothing, in an effort to hasten their departure. Thus G‑d made His promise to Abraham, that his descendants would leave their exile with great riches, come true in every detail.
Leading the Jewish people on their journey during the day was a pillar of cloud, and at night there was a pillar of fire, giving them light. These Divine messengers not only guided the children of Israel on their way, but also cleared the way before them, making it both easy and safe.

Why not 1446 BCE?
1 Kings says Solomon began building the Temple in his fourth year (approx. 966 BC). This "early date" view, often associated with Pharaoh Amenhotep II, is supported by various chronological, archaeological, and jubilee cycle calculations.
1 Kings 6:1, Judges 11:26, and 1 Chronicles 6:33-38 suggest the earlier date than the alternative 13th-century (approx. 1290-1260 BC) view.
when did Joshua first cross the Jordan to take the first city.... Jericho? About 1240BC. There was no King before Saul... later.
Our dating of the Exodus is based on the calculations of Rabbi Yosi from the 2nd century in the work Seder Olam. He used Biblical descriptions and Talmudic calculations, working backwards from his era and the destruction to the 2nd Temple to create a consistent timeline stretching all the way back to creation. See here
Based on his calculations, the Exodus occurred in 1313 BCE.
Why not early Spring, circa 1406 BC.
The crossing took place on the 10th day of the first month of the Hebrew calendar (Nissan), just before Passover.
[1 Kings is 1 Melachim]
They crossed opposite the city of Jericho. The Jordan River was in flood season (springtime harvest) when they crossed on dry ground.