What year did the Hebrew nation with Joshua cross the Jordan river
into the promised land?
According to the Ancient Seder Olam, it was on the 10th of the month of Nisan, in 2488 or 1407 BC that Joshua took Israel across the Jordan River. This took place 40 years after the exodus from Egypt.
The month of Nisan is the first month on the religious calendar.
Joshua 3:13-17 (NKJV)
And it shall come to pass, as soon as the soles of the feet of the priests who bear the ark of the Lord, the Lord of all the earth, shall rest in the waters of the Jordan, that the waters of the Jordan shall be cut off, the waters that come down from upstream, and they shall stand as a heap.”
So it was, when the people set out from their camp to cross over the Jordan, with the priests bearing the ark of the covenant before the people, and as those who bore the ark came to the Jordan, and the feet of the priests who bore the ark dipped in the edge of the water (for the Jordan overflows all its banks during the whole time of harvest), that the waters which came down from upstream stood still, and rose in a heap very far away at Adam, the city that is beside Zaretan. So the waters that went down into the Sea of the Arabah, the Salt Sea, failed, and were cut off; and the people crossed over opposite Jericho.
Then the priests who bore the ark of the covenant of the Lord stood firm on dry ground in the midst of the Jordan; and all Israel crossed over on dry ground until all the people had crossed completely over the Jordan.
Jamieson-Fausset-Brown Bible Commentary
Jos 3:14-17. The Waters of Jordan Are Divided.
14-16. And it came to pass when the people removed from their tents, &c.—To understand the scene described we must imagine the band of priests with the ark on their shoulders, standing on the depressed edge of the river, while the mass of the people were at a mile's distance. Suddenly the whole bed of the river was dried up; a spectacle the more extraordinary in that it took place in the time of harvest, corresponding to our April or May—when "the Jordan overfloweth all its banks." The original words may be more properly rendered "fills all its banks." Its channel, snow-fed from Lebanon, was at its greatest height—brimful; a translation which gives the only true description of the state of Jordan in harvest as observed by modern travellers. The river about Jericho is, in ordinary appearance, about fifty or sixty yards in breadth. But as seen in harvest, it is twice as broad; and in ancient times, when the hills on the right and left were much more drenched with rain and snow than since the forests have disappeared, the river must, from a greater accession of water, have been broader still than at harvest-time in the present day.