Victorious German Empire in WWI plus a collapse of Austria-Hungary would have Germany annexing Austria and significant amounts of Bohemia. Combine that with other German gains (a bit of land in France, Luxembourg, maybe even the parts of Luxembourg which are now in Belgium), and it isn't too unreasonable for Germany to have over 120 million people, especially without a WWII.
A Poland-Lithuania wank might be able to do this too, assuming no Deluge and continued Polish success where Poland ends up with all modern Poland, all modern Ukraine, parts of western Russia (including Kaliningrad, obviously), Lithuania, Latvia, Estonia, etc. 21st century Poland-Lithuania might be able to have over 120 million people, although that might be a bit more of stretch than Germany and would probably take more immigration.
But for a post-1900 POD, only the German Empire could really pull that off.