Attacking Poland first. Playing Carol II of Rumania like a fiddle could have provided a way to stick the shiv in Stalin’s underbelly while avoiding an immediate war with Britain and France.
In the grand scheme of things, Poland wasn’t important yet by attacking it, Germany ended up in a war with Britain and France. Sure, that didn’t play out well for France and Germany fairly quickly had their western front secure but the continuing war with Britain distracted Germany and drew off resources while the real prize, the USSR, sat unmolested.
Bringing Britain into the war allowed a second front, Africa to come into play while Germany’s real intent was on the east. And that’s where Hitler should have started his fighting, but not with Poland.
Hitler wasn’t going to be content to just sit in central Europe without expanding and the true threat to his goals was the USSR. So how to engage them without bringing the French and British into the war? By doing an end around Poland and using Czechoslovakia and Hungary as springboards to jump into Rumania and then to the Ukraine.
By 1938, Rumania had pretty much fallen into a dictatorship under King Carol II who saw advantages in siding with Germany vs. Rumania’s traditional allies. In a game of statesmanship, Hitler vs. Carol II, I’d put my money on Hitler being able to persuade Carol II that there was Rumanian glory to be had if German troops were allowed free passage through Rumania, even more if the Rumanians joined the invasion of the Ukraine.
In the worse case if this all fell through, heck, just invade and keep going east. By taking this approach, Hitler would have avoided the treaty tripwire that his Polish invasion set off. Certainly Britain and France would have been alarmed at an invasion of the USSR but it seems a tough sell to believe they would have declared war on Germany when nothing said they had to.
Germany would have had their one front war though admittedly they’d have had to watch their western back. September 1939 would be a pretty sucky time to invade the Ukraine with the winter around the corner but that just meant they would have an additional 6–7 months to get ready for war. And to schmooze Stalin and discuss plans to carve up Poland while measuring his jacket to see what size knife in the back would best fit.
I don’t know that there was a winning approach for Hitler but with hindsight, bringing Britain and France into the war for sort of a small prize like Poland seems like the wrong approach. Better to find a way to deliver the KO to Stalin at the start and then think about the West. After WW1, neither the Brits or the French were anxious to lose another generation so they had motivation for yelling loudly but carrying a small stick if Hitler expanded east.
Obviously they and the US would have gone to more of a war footing and maybe they would have provided aid to Stalin but that’s a far cry from engaging in actual warfare and drawing off resources as actually played out. Attacking Poland ultimately turned out badly for Adolph. Attacking the Ukraine through Rumania might not have played out better but from the Fuehrer’s point of view, it could have hardly turned out worse.