Alternative...
The USN trades fire with the Germans near the Philippines during the War of 1898, prompting Germany to declare war on the U.S., after cutting a deal with Spain. Three powers are then at war. Perhaps, France and/or Britain declare for the United States, and soon a world war is underway. With the Great Game underway, the Russians are persuaded that the British are distracted, so they join the war citing the Three Emperors' Pact. Austria-Hungary gets in then too.
Germany, Spain, Russia, Austria-Hungary vs. United States, British Empire, France.
If you want a Great War in the 1910's with the US involved in the start of it, this can be a starting point that later leades to the US involvement from day one.
Off of Manilla: Dewey's forces fight (and IMHO, defeat) the German navy. War is declared on both sides. Germany and Spain are now co-beligerants....not something calculated to give France warm fuzzy feelings.
USN: 5 Battleships, with 5 more launched and fitting out, due within 2-3 years AT PEACETIME FITTING OUT RATES, and 3 more authorized, so materials probably allready being assembled. The forst 4 are ocean capable, but not great for deep sea fighting.
5 Monitors--big gun ships, useful only for coast defence...but still useful for that.
Germany has 9 relatively modern battleships, with no ore on the ways, plus a pile of small coast defence ships.
However, neither side could effectively project power due to lack of bases. As the nations of Europe start making noises about taking sides, with Britain's sympathies with the USA (to contain Germany) the chances for a war on a grander scale start looking very real. A few cruiser actoins in the Atlantic, and some commerce raiding, comprise the majority of the war before peace is negotiated.
But now, the USA is well aware of how expensive not having a good cruiser fleet to back up the battle line is, and American yards do build som scout/raiding cruisers. And...with Germany hostils, the USN is seen as more important than when there were no great power enemies. USS Michigan and HMS Dreadnought hit the water at about the same time, but Dreadnought is still completed faster.
Invincible and Von der Tann are matched by USS Newcastle, a battlecruiser that's slower than the Brisith version, but better protected, and built, like the British ships, for long range sailing.
While understanding the American naval build-up, it's still alarming to the Brisish, since ships aimed at Germany can just as easily be aimed at them. To ease British concerns, the USA promulgates a policy that "The United States Navy will match the German Navy on a ship for ship basis in capital ships."
This states clearly to the British that the concern is Germany...but that's still a LOT of warships. Japan, of course, is concerned because the Americans are stationing some heavy firepower (mainly older battleships, but with one or two battlecruisers) at Manilla...sufficent to deter any adventures by the German Far East Squadron, and to catch them if need be.
By mid 1914, the USA has the world's number two navy, and continuing harsh feelings towards Germany. Britian is worried about both the US and German build-ups, (but more worried about Germany's, as a dominant power in Europe is a terrible idea) and Japan is worried about the American intentions...and knows that taking American territory away is not really an option.
Now, there could be an incident in the Far East between German and American forces, a trade dispute, a clash between Japanese and American or German forces, a ship blowing herself apart in anotehr nation's harbor, or more.
Assuming that the US is involved from the start, it could get even uglier. Both Japan and the USA rush to seize German islands..and the American and Japanes fleets start shooting at each other over a choice piece of real estate.
Lots of different possibilities here...