The main element of support was saying that they would join the fight on behalf of Austria-Hungary if Russia joined the fight on behalf of Serbia. Without other states being involved militarily, German support would have remained diplomatic. Furthermore, when Serbia responded to Austria-Hungary's ultimatum, the Kaiser thought Serbia's response defused any justification for a war, though diplomats did not pressure Austria-Hungary to accept it. It was Austria-Hungary's choice, albeit a choice that had probably been made before the ultimatum was even sent. I think elements of the German government beside the Kaiser were somewhat more hawkish, though.

It was furthermore Germany's desire that if Austria-Hungary attacked, that they would seek to limit the scope so as not to get Russia involved (though saying simultaneously that they will fight alongside Austria-Hungary if Russia is involved is probably conducive to not taking that advice very seriously), so it's not like it actually wanted a war involving the larger powers, because they knew such a thing would be an existential hazard, and that's what it became. I think even if you want to say it is mainly Germany's fault that the war started, it is a still further and much more unjustified claim that it wanted to "provoke a large European war" when it knew that such a thing would have a good chance of destroying it. If anything, it wanted wars that were limited in scope to more securely benefit its position, though it ran the risk of being party to the start of larger conflicts and that's exactly what happened.

To be more clear, I'm not saying the Kaiser was an innocent smol bean, he was an imperialist monster, I just think that the culpability lies with many countries and their imperialist monsters, including Austria-Hungary more heavily than Germany. If you want to say that Germany was simply a contributing member to the war starting, of course you are right, but the phrasing "Germany started with war" suggests it bore overwhelming responsibility, especially in the context of also saying it started WWII, where it is obviously the main state at fault to an overwhelming degree. For the lead-up to WWI, Germany absolutely influenced the calculus in ways that were mainly prone to escalation and the invasion of Serbia, but I don't think the two cases are comparable. If anything, I think it's the immense guilt of WWII that has led to the broad long-term acceptance of the Versailles characterization of WWI, where otherwise such a thing might have been written off for what it was, the victors of the war declaring an exaggerated version of the history to benefit their own image, an extremely normal thing to do at the end of a war.

But again, I'm not an expert, I could be missing vital information or context, I just have made some attempts to research this subject critically and this seems very strongly like the most solid conclusion.