The reason I ask is that it seems like one of the biggest setbacks for the German army was their small size. Had they recruited and attempted to build armies from the countries they conquered, I could've seen them being even more of a danger to the rest of the world. I am not extremely well versed in history so apologies if this post looks very lay-man.
Yes they did, due to internal German politics the Waffen-SS could not legally conscript German citizens as that was the sole privilege of the regular armed forces. Thereafter they used recruitment from occupied territories as one of the ways to gain manpower. Occupied European countries also had far right/Fascist movements during the pre-war period and thus offering up some young men who are ideologically inclined to fight for the Nazis against the Communists on the eastern front.
During the war several SS divisions division were recruited from occupied western Europe. The elite SS "Wiking" division (it had 15,000-20,000 men at any given time) for example was recruited from citizens of occupied Norway and the low counties, as well as volunteers from Sweden. The SS "Nordland" division was also largely filled by mostly by volunteers from Scandinavian but also included Spanish, French, Estonian and other nationalities. The "Nederland" division was composed largely of Dutch volunteers.
Those are just some examples of foreign divisions. The SS also had recruited from Muslim populations in the Balkans, such as Albanians. Himmler also instituted mandatory conscription in the occupied Baltic states like Latvia. All in all there were more than a dozen foreign foreign units in service with the SS.
As the war progressed the Germans even took to recruit captured Soviet PoWs to form anti-Communist Russian divisions. The Wehrmacht also recruited hundreds of thousands of men in occupied Soviet territories as auxiliaries to be used in second line roles, i.e anti-partisan operation and garrisoning duties. Both on the eastern front as well as other theatres of war (i.e Yugoslavia).
Despite the brutality of the Nazis and their racial supremacist ideology, they were able to find collaborators in every single country they occupied. Those include men who fought willingly for the Nazis: both for the regular armed forces and the Waffen-SS. It is perhaps ironic that the Waffen-SS, a force whose ideology is Aryan supremacy, have so many members within it who are considered subhuman according to that ideology.