It would have been very difficult for such a multitude wandering around out on the desert to have lived for more than a few days.

​Yes and the same could be said about one person out on the desert. They are forgetting God, Who supplied water, meat (quail) and daily bread (Nehemiah 9:20). They believe that encampments of such a multitude would have left some sort of “trash” for them to follow, but they are still trying to figure out which route the children of Israel were on. “Yea, forty years didst thou sustain them in the wilderness, so that they lacked nothing; their clothes waxed not old, and their feet swelled not.” (Nehemiah 9:21) There was no thrown away, worn-out clothing, no piles of leftover manna as it melted (Exodus 16:21), and they left no “soda bottles or gum wrappers” for them to follow. Israel had "flocks, and herds, even very much cattle" (Exodus 12:38), thus they would have had animal skins (that would have deteriorated) in place of pottery.
         As others have brought out, the Israelites the critics are looking for never existed, because they do not believe God provided for them, but the truth is Israel “lacked nothing”! Their inability to find something is what they offer as proof! They only recently found (2002) the “workers’ village” for the pyramids of the Giza Plateau. It is estimated this town housed 20,000 people and was built out of bricks, whereas the children of Israel lived in tents. And this discovery only came after they had searched every inch of the Giza Plateau for the last two hundred years of archaeology.