The crossing of the Jordan is part of the Conquest narrative created by later Israelites, perhaps in an attempt to differentiate themselves from their Canaanite brethren. One of the scholarly hypothesis current among academics (although it’s been a while since I’ve done any reading in this area) is that the Israelites were indigenous Canaanites. In this case the crossing itself is a piece of fiction. Perhaps someone else can speak more to this point.
I think archaeologically, as with other stories in Genesis and Exodus (See the works of Dever, Finkelstein), the crossing of 624,730 males (Num 26:51, 62), plus their wives, daughters, sisters, children, and livestock, not to mention the legendary “spoils of Egypt” that this crew has been laboring on their backs for 40 years nor for that matter the 7.5 tons of gold, silver, and bronze that was used in establishing the mobile Tabernacle compound that this motley crew was also carrying around with them (for a good read see http://contradictionsinthebible.com/gold-for-the-golden-calf-or-the-tabernacle/), is just an “event” that is missing from the archaeological record. More to the point, this is ancient literature proper that we are reading and it is in the context of ancient literature that we should understand these texts, or here this story. Why and when was it written? What purpose did it serve? At what festivals was such a story recited and why? Etc.
Another tidbit of info: the biblical record itself preserves a variant story on the Hormah tradition. Recall that it was on account of the Israelites defeat at Hormah (Num 14) that they had to turn tail, head south toward the Red sea, travel north outside of and around Canaan on the east side of the Jordan (and according to one tradition around Edom and southern Moab), and in short invade Canaan from the east by crossing the Jordan. There is a horribly misplaced version of the Hormah battle where the Israelites are victorious, and a later redactor placed this variant version in what is now, in the redacted JP text, an “event” that happens in the 40th and final year of the wilderness campaign (Num 21:1-3). So according to this victory at Hormah, which is a city well into the territory of what will be the territory of the tribe of Judah—that is the Israelites successfully enter/invade Canaan from the south according to this tradition!—a Transjordanian trek and invasion from across the Jordan wasn’t even necessary. My point? There are, or is, a variant version of the conquest in the Torah literature. In all reality, both of these Hormah traditions (the defeat of Num 14 and the victory of Num 21) most likely represent real battles during a later time period (9th-8th centuries), that were then used as part of the creation of the wilderness narrative, and it so happens that the victory at Num 21 was ill placed, since by its very feat the Israelites had now successfully invaded and were in Canaan proper! For more, see also http://contradictionsinthebible.com/when-do-the-israelites-enter-the-promised-land/