The republic and CIS conflict was inevitable. Their political friction existed with or without Palpatines influence. It was only a matter of time before thing came to a boiling point.

We don't get to see things from Palpatines perspective so it is hard to know what influence he did or did not have over them, but I am willing to bet that he WAS the reason the war started when it did, but I also don't think that's a bad thing.

Palpatines whole plan was to use the war to gain power through the senate, he had already invested a lot of time which would have been wasted if the CIS won.

From that we can guess that Palpy encouraged the CIS to attack earlier, but never planned for them to truly succeed, just to be a big enough threat that the Republic would be stirred out of their stagnation.

However even attacking at the point they did, the CIS put up a hell of a fight, so I don't think it's unreasonable to believe that if Palpatine had NOT encouraged them to attack earlier and they had instead been left to accrue more power and prepare more that they would have actually won, and crushed the republic entirely.

This seems extremely likely considering that Palpatine ALSO organized the clone armies. And without them the republic would have been entirely fucked even as things are.

The other influence I see him having is pushing them more in the direction of Robot Soldiers. Something that doubtlessly prevented a lot of innocent bloodshed on the CIS side. (Bloodshed he ALSO prevented for the republic by using clones rather than normal soldiers).

So Palpatine 'caused' a war that would have happened anyway by ensuring that the enemy would be defeatable and that as few civilians would be harmed in the conflict as possible.

Is that Shady and Power-Seeking? Yup.

But if Palpatine truly believed that the Republic as it was would continue to be vulnerable to this kind of thing (something that IS supported by what we see in canon) then he might find it justifiable, let the child scrape his knee so that he doesn't break his leg later and all that. A million deaths now weighed against trillions of deaths in the future would seem to be a rather obvious choice.