I don't think it was so hard. Wilson campaigned for his second term by promising to keep us out of the war. Were it not for the manipulations by the British, et al, we likely never would have gone to war at all. I argue with an Austrian from time to time that still claims the Lusitania was carrying explosives to England, and that's why it sank so quickly.
Nor do I think that the assassination of Ferdinand was necessary. Germany had invested in its military, and spent more on that than they spent on trade with France, so they looked to their legions as a solution, rather than restraining their legions to retain trade with France. Britain had more trade with France than Germany, so would side with France.
Plus they had the experience of their previous victories against France, and were likely feeling arrogant. Seems to be a common problem in wars I think.
The Lusitania was carrying munitions but not of the kind that would have subjected it to attack. Even if it was carrying munitions, naval attacks had in all circumstances to make provisions for the passengers.
Unless you were a German. They didn’t intend to lose, and if they won, the rules wouldn’t matter.
The rapid sinking had something to do with the torpedoes.