Socialism is in the name though

Considering private properties and private for profit enterprise was encouraged under the Nazi regime until it was untenable due to war constraints says you're wrong.

Encouraged? Is that what you call it when the state decides who has what, how much, for how long, when, and what they'll be doing?

So long as you were a full blooded german you had the right to own and/or operate private property. If you were a Jew or any other minority your rights were revoked. Once again this was true until the war necessitated the state run the economy. As happened in all of the waring nations incurring the US.

And what was the exact process of what happened in Germany to get to that point?
Walk through it man. And yeah, FDR was the original fascist, this is news to nobody. He didn't even have the decency to wait for the war as an excuse.