It may be that any US president would have done the same thing.
No evidence of that. Several Presidents have avoided starting wars for that or similar reason (Clinton, for one).
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If he would think war is useful for the elections, he would have already started it before, when the US drone was shot. The impeachment does not look dangerous at all, too irrelevant to start a war.
Trump had not consolidated illegitimate power earlier, and despite his best efforts (on the Mexican border, in Venezuela, in SE Asia, with Yemen or Qatar, with Iran, via the military budget in the US, etc) was unable to gin up a sufficient reactionary justification. ( A US President cannot start a war merely by means of the legitimate powers of the office.)
He isn't competent at this, you understand - he wants to have a small war, drop big bombs on little people, repopulate Gitmo, etc, but has almost no experience with military force, and little knowledge of military issues. He also doesn't know any history - he has no idea how wars started in the past, what happened to those who started them and why, any of that stuff. Meanwhile, he doesn't know who to get advice from in dealing with foreigners, and has been purging his administration of competence and diplomatic expertise in foreign policy.
So, as the lefties have been pointing out for years now, the risk with Trump is accident or unforeseen mishap - some stupid mistake of his belligerence-based and military-backed foreign dealings that escalates and spreads to somebody who is cornered and can do real damage to the US.
If he ever does manage to start a war, touch off a nuclear exchange, motivate a serious and well-supported terrorist campaign against the US, etc, it will probably be by accident - which is also the only way it will end, unless the US can find some way to take the Republican Party out of government.