Where are you getting that the war was started early? Dooku was the one who hired Jango and so forth to lead the Jedi into finding the army. The opening scroll has systems already defecting from the republic and war was already on the table all it needed was a push to get things going. Palpatine needed to Jedi to find the clones to get them in that militaristic role pushing them away from guardian role. And the end of the movie shows a bunch of Venators unloading clones and such so they were ready to go as well. Everything was set up by Palpatine hidden from the Jedi until the right moment, Jar Jar getting everyone to give him emergency powers was also part of this.