If you read the articles by the Stavka, their aim was clear -- get Galicia from the Austrians and stream south to wrest Constantinople from the Turks
It was not ready for war and the Central Powers new this. --- I don't think anyone quite knew that -- the Russian Empire was not prepared for a modern long war, no one was -- everyone believed that the war would be over by Christmas
The Central Powers definitely did not know this -- on the contrary they knew about the number of conscripts in the Russian army -- 2.5 million men and trembled. Combine that with increasingly better weapons from France and England and the Germans were terrified that by the 1920s the Tsardom would be an unstoppable horde from the East.
I believe you are approximately correct. The Germans decided to precipitate war because they thought it was “now or never.” They believed, quite possibly correctly, that the odds would go increasingly against them as the Russian Empire modernized.
Russia advanced tremendously in the decade before 1914. Another decade like this and the Germans would have a more or less modern enemy on each flank. Better to strike now while Russia is still a third world nation.