What if Hitler didn't declare war on the Soviets until after WW2?

If Germany didn't declare war on the soviets, the soviets would have declared war on Germany. The minute the soviets started to feel threatened by the vast and ever growing German empire they would choose to declare war, resulting in a war on two fronts, which would lead to the Third Reich's eventual demise just like what happened in our 'timeline'. The real mistake Hitler made was declaring war on the U.S which put the final nail in his coffin.

The strategy you're suggesting would have been impossible to execute. Hitler invaded the USSR when he did because he knew the war in the West was unwinnable. The failure of German attempts to achieve aerial and naval superiority in the Battle of Britain put an end to Hitler's hopes of swiftly eliminating the British threat. The only way to crush the British Empire was to seize strategic British possessions (such as Malta, Cyprus, and Egypt), to cut her off from her colonial supply network, to strangle her economy and resources with a general naval blockade, and to demoralize her populace with a heavy strategic bombardment campaign. In the meantime, the Royal Air Force and Royal Navy were exerting the same kind of pressure on Germany, and the British had a lot more stamina than the Germans when it came to withstanding a virtual seige.

Therefore, the only way to keep the Reich stable was to gain access to the vast natural resources Eastern Europe had to offer. If Germany could push into Russia and knock out Moscow, Leningrad, Stalingrad, etc. then they might be able to eliminate the Soviets' capacity to resist and to harness the bottomless supply of resources found therein in order to outlast Britain.

That said, if the Germans did in fact decide to postpone their invasion until they could deal with Britain, the war would have lasted much longer, and most of it would involve a colonial struggle for the Mediterranean, North Africa, and the Middle East in addition to the mutual strangling efforts taking place across the English Channel. With increased help from the Germans, the Italians would have much more success their own theaters of operation. They could seize Malta, Cyprus, and the Suez without too much trouble, damaging Britain's chances of regaining control of Iraq and the Levant. If the Italians successfully took control of the Suez, an attack and/or blockade on Britain's colonial possessions in Arabia and South Asia would not be out of the question.

If the US got involved, which they probably would, they might be able to go through with Operation Overlord or something similar. At that point, you can't expect the Soviets to stand idle as the Western powers take over Europe, so they'd have to get involved at some point. And with a well-rested army standing by, they might be able to push farther into Europe than they otherwise would have.

In short, Germany would probably lose.