Some argue that Germany invaded the USSR to keep its war machine going, that it was going to run out of oil in August 1941. But the Germans found oil fields that were only destroyed, and didn't get a small one pumping (Maikop) until 1943.
So how were they making up the deficit? Especially since Barbarossa would surely increase the demand for oil and even bring the deadline forward?
One of Nazi Germany's main sources of oil was the Romanian oilfields and refineries at Ploiesti and Câmpina. In March 1939, they negotiated a very favorable trade agreement with Romania which made them the main importer of Romanian oil (something like 50 percent of Romania's total production). I found the text of this agreement but unfortunately I don't have an English translation of it. Romania's production wasn't sufficient to fuel the entire German war effort of course, and that's part of why Germany increasingly relied on their synthetic fuel industry. Germany also didn't hold up its end of the trade agreement (especially coal deliveries), which Ion Antonescu was pretty unhappy about.
The Americans launched two air raids against the oil refineries in Romania in 1942 and 1943, but they didn't manage to shut down production long term; they destroyed about 40-50 percent of Romania's production in 1943 (sources vary a bit) but it was restored within a few months. It wasn't until 1944 that they were able to make significant headway bombing Romania (once they got access to airfields in Italy), but by that time, Romania was only a few months from collapse because of the Red Army's advance from the east.