I think the first real inkling of that was shortly after the ACW, when one of the monitors was towed across the Atlantic and displayed in European ports. That shifted the balance of naval power practically overnight, as Europe suddenly awoke to the fact that a lot of their best ships had just become obsolete. During the late 1880s or 1890s, the US went from still importing specialty steel from the UK for more demanding applications to exporting its own high-grade steel.Which was working in the 18th century when outside Europe you had nothing but "worthless wasteland"... in the 20th century the British failed to realize that it is the US, which is endangering their position as the dominant world spanning empire.
Before WWI, the US was viewed as just another source of manpower to be armed and led by the superior Europeans. By the end of the war, the sheer scale of industrial power in the US had clearly grown to where they were no longer a second-rate agricultural nation, and heading rapidly toward the top spot, but by then it was already too late for the UK to change the situation. The post-war naval treaties reflected the reality of US naval power. By WWII, the US was indeed the senior partner in any alliance. If WWI never happened, or happened in such a way that the US never got involved, it might have been another few decades before that reality became blatantly obvious.
From what I've come to understand, WWI didn't happen immediately after the assassination, in part because Hungary initially blocked Austria-Hungary's vote to declare war, and had to be persuaded and pressured into accepting it. Further expansion of Austria via the conquest of additional territory would have reduced the already limited representation of Hungary in the A-H Parliament, so it was not in Hungary's interests to allow it.