You're spot on, but it actually didn't start with the Nazis; Hitler just adopted it as part of his foreign policy (I believe he even writes about it in Mein Kampf although I haven't looked it up). The official name for this philosophy is Lebensraum [1] and it's widely recognized as having started in the late 19th century, decades before WWI errupted, when Germany had a growth spurt and started to feel the pain of over population. However, how much Lebensraum had to do with the first war is unclear, since the Princip/Ferdinand situation was the huge spark that started it. That said, there was a whole plan assembled during WWI based on it called Septemberprogramm [2] with the goal of expanding German territory for resources.

[1] https://en.m.wikipedia.org/wiki/Lebensraum

[2] https://en.m.wikipedia.org/wiki/Septemberprogramm