I am plodding through three possible PODs:
(1) TR runs for a second full-term in 1908, he eschews the "third-term" in 1912, likely a Republican wins but Democrats make inroads and possibly TR influences Europe in peace talks regarding the second Moroccan crisis or involves the USA in Mexico on the eve of WWI; (2) the assignation occurs but with first assassin only so it is more obscure it is a conspiracy, common knowledge is that Serbs are behind it but no trail into Serbia and by inference to Russia, A-H makes less onerous demands and no Blank Check, Russia rattles sabre meekly if at all, the spark averted but Greece intercepts and sinks the Ottoman battleship, Europe on edge stumbles backwards into war; (3) from first two PODs Moltke shies from a France first coup de gras and choses Russia first, Germany fails to violate Belgium in 1914 and without coastal ports has weaker position to launch USW. Each affords one with a close on to out known timeline with many butterflies to both open and close doors to alternate outcomes.
I can draw foggy lines to British Empire never entering war or with less enthusiasm, Russia still sets events in motion with a mobilization, FF still dies, the war ends in 1914 or a white peace in 1918, the Italians stay neutral or not, Mussolini or not, and so on. But without WWI the USA goes off in a very different orbit. I am questioning the passage of Prohibition, the Great Depression, whether there is a Sino-Japanese War and if the USA goes to war with Japan, and so on as butterflies beget caterpillars that give yet more butterflies.