Although your question is ambiguous as could be, I'll do my best to answer. The Nazi's had indeed invaded countries by Jan 1940, beginning with the Austrian "Anschluss" in 1938, they invaded Austria. Then following the Munich Agreement in 1938 invaded Czechoslovakia. It was when the Nazis invaded Poland on 1st Sept 1939, that Britain and France declared War. What followed was conned a "Phoney War" as neither the Allies nor Germany invaded any country. This came to an end in April 1940 when Germany invaded Netherlands, Belgium and subsequently France. So yes you are right to a degree that WW2 had not fully begun by Jan 1940.
Hope I helped :)