Most of Europe was locked into alliances with several nations which would force them to join a war their ally entered. As well as that Germany (who had only existed for about 50 years) was in an arms race with Britain and keen for an oppurtunity to prove themselves/expand

Europe at that time was sitting on bomb. Any spark could have it ignited, and there wasn't a lack of those. Many territorial claims were still unresolved, like alsace-lorraine/elsass-lothringen with France and Germany, Italian irredentism, the whole Balkan being a mess of nationalities not corresponding to borders. Although WW1 would not have needed this assassination to go to war, I think it would still have been possible for WW1 not to happen. Things are not always as set as we think in history. Thing is, it would have required a team of bomb-disposal amateurs that hate each other and question the point of the mission, to actually defuse that bomb.

One must also consider the underlying atmosphere of nationalism that permeated Europe at the time. According to "the class of 1914", there was general excitement when war was announced. Citizens romanticized war, viewing it as a glorious way to have an adventure, see the world and prove their countries value. Indeed, there was such public support for taking action that leaders were almost pressured into starting the war. One can view the assassination as a catalyst which sped up the process of starting the war, but national tensions brought on by conflicting ideologies, an outdated alliance system and the naval arms race between Britain and Germany were th largest effectors of conflict. It probably would have started regardless, not least because Austria-hungarys annexation of Serbia was a powder keg which the Russians were watching carefully. Also, there was no previous experience with modern warfare (machine guns, bolt action rifles etc) so people didn't know it's horrific cost. If there would have been no public support, then waging a war would have been far more difficult. Hope this helps