All the following information is from this book:
http://www.amazon.com/Princeton-Studies-International-History-Politics/dp/0691015953
The war really cannot start earlier for Germany either because of her limited siege artillery. AH only managed to get her 24 mortars finished in 1913 and Germany still didn't have her 2 big Berthas yet. Yes, she did have several 350mm 'Küsten Möser' that really were siege pieces, but they weren't really all that mobile. Plus the Kiel canal didn't get finished until 1913 IIRC either.
Now a slightly later start to WW1 is interesting; if the war starts in 1915-16 Germany's 'window' is still open and relatively her forces are will be getting stronger, as she was forming two additional corps for peace time. They would be ready by the end of 1915 and more experienced by 1916. Also her nitrate plants would be ready in 1915-16 before the war.
Meanwhile France would in 1915 still be disorganized by her 3 year law about conscript service time and only in 1916 would she start to realize any benefits from it. However the liberals were rallying and would likely have taken down the 3 year law (the so-called Cadre Laws) in 1915 anyway, further disorganizing them. However the French would have more modern howitzers in 1915-1916, but probably no more than 100.
Russia was also rapidly improving, but was having trouble spending the money on the army. Even though the government passed a bill to allocate money to expand the army, it wasn't getting spent on time, there were major production delays, both domestic and foreign, and worst of all civil unrest was increasing and may well boil over before 1916, which would make Russia much less effective in battle. Also in 1915 she was adopting a new mobilization plan that would likely make mobilization far less efficient for a year or two as everyone became familiar with it, as it radically changed vs. the previous plan. The only truly bright spot for Russia in the 1915-1916 period would be the increased rail capacity and a quicker mobilization of her forces.
AH is an interesting case. Her artillery modernization program would be complete in 1916 and leave her forces with 60 artillery pieces per division, including 36 howitzers. Each corps would have another 24 heavy howitzers and it looked like the Hungarians were going to allow it through because the Honved was getting it too. Now there were problems in that the Hungarians were delaying Combined army recruits from departing to training again and were starting to contest money to the army again because tensions were subsiding, but who knows how that would play out. A later start means AH has more men trained after the 1912 conscription expansion law has more time to take effect (an extra 50,000 men a year IIRC).