There is quite literally an entire section in the FAQ dedicated to the economics of Nazi Germany. There is this excellent overview by /u/volksgrenadier, or this great cursory rundown of the nazi economic policy and military spending by /u/ponter83. There there is this very informative post by /u/caherdaniel that explains how the political landscape in Germany affected the economy of the country and vice versa and then there's this one by /u/vonadler that details just how much gold alone Germany confiscated from annexation and occupation.

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If you want a very short answer, he didn't. The german rearmament had the german economy constantly balancing on the verge of collapse. Had Germany not annexed Austria and Czechoslovakia, captured gold reserves from many other countries AND used the MEFO-bills to finance key parts of the rearmament it could never have been done. Even with all this, the German government went into the war with a national debt comparable to what the US came out of the war with.