Does anyone know if a deer permit along with the apprentice license is required to deer hunt for a non-resident youth during the first firearm season? I would assume so , but I couldn't find this information on the IDNR website.

If you have completed a hunter safety course, you can get a regular license instead of an apprentice (you have to be supervised if you have an apprentice license). But you do need one or the other (deer permit alone is not sufficient). The pricing sheet shows apprentice licenses are available to nonresidents, so the answer appears to be yes. You also need a habitat stamp ($5.50). Some of this is explained in the footnotes to on the page of the hunting digest that shows license prices.