Per Hashem’s command, Yehoshua has the Jews circle Jericho and the Kohanim circle Jericho and blow their shofars. There are lots of sixes (a physical number, like the six days of the week), lots of sevens (a spiritual number, like Shabbas), and, after the circling, the shofar blasts, and the shouting of the Jews, the walls of Jericho fall. The Jews have a military victory and the catalyst of this victory is blatantly spiritual.
A legitimate question is, Why does Hashem have the Jews take the silver, gold, etc. for the treasury, for the Kohanim, and kill the women, children, animals, everything else? The answer may be that Hashem wanted this military victory, the first military victory post-Moshe, to be a spiritual victory. The battle would be spiritual, the spoils of the battle would be spiritual. The battle was most certainly spiritual. The spoils, by making the silver, gold, etc. into holy objects for the Kohanim, are spiritual. The women, children, animals, etc. of Jericho are also spoils but they are not spiritual. And, to include them within the spoils would taint the spirituality of this unique victory. This battle was, so to speak, all spiritual and all for Hashem.