It is not impossible, but very difficult. One very bad blunder by the French commanders would probably be enough, such as the 5th Army surrendering or the French attacking into A-L with either more forces or for a longer time period.
The German problem was they were outrunning their logistics even by the time of the Marne. You can read the first few chapters of Falkenhayn book, which is free on line, for a good description. So without some French blunder, the Germans were close to having to take an operation pause due to the supply situation. As these battles unfold, A-H is collapsing in Galicia, and will require help by early Spring to stay in the war. East Prussia is being attacked and it will be hard to avoid sending any reinforcements. We also know that Urban terrain favors the defender, and the French would throw all available reserves into saving Paris.
So with all these facts, the Germans have a narrow time window to accomplish series of open terrain wins and a major urban battle, all with limited supplies. It is not impossible, just exceptionally difficult, and IMO, impossible without a major French mistake. A more realistic, best-case scenario for Germany would be holding the Marne, possibly conquering a lot more of Flanders (Amiens, Calais), and possibly destroying a French Army. Then the Germans have to turn east in 1915, but they will gain a chance to win in 1916 in France.