Germany "had" to invade Poland because its economy was overheating and was close to breaking point. Ever since mid 1930s Germany was running a massive deficit due to focus on armaments rather than consumer and export goods. To put it simply, it was spending money on things it wasn't exporting and wasn't producing much to export and gain money. It was running out of reserves of hard currency and gold and received a boost by Austrian takeover but by 1939 that was gone as well. So it was either continue with existing policies and crash economy or go to war to gain further resources for additional boost. Hitler chose the latter.

A good analysis of German economy and dilemmas it faced after Great Depression and under Nazis is The Wages of Destruction: The Making and Breaking of the Nazi Economy by Adam Tooze. While it draws some questionable conclusions regarding war economy and performance during the war it offers fine insights into early development.