Obtaining Spain's former colonies as territories began the process of integrating the United States into mainstream world politics. Before too long, the US was already intervening in Central America and the Caribbean, began participating in coalition efforts to stamp out the Boxer Rebellion in China. All of a sudden, they had interests that they needed to address, something the US never had before beyond their own frontier in North America. Even obtaining Hawaii and Alaska was still on the fringes of world affairs.
The US had a policy of neutrality towards European affairs, with respect to the Monroe Doctrine. Plus, they had all this new territory they had acquired from France that they had to explore and settle. That was enough to occupy American energy. But once the frontier was closed, all that energy wasn't just going to evaporate, the US wasn't just going to rest on their haunches. The US was still hungry. She knew in her heart she was a heavyweight, but an untested one. The Spanish American War was in a way, the Americans' step up, to see if they can truly hang with the great powers of Europe. Spain was essentially a hand picked opponent, one that the US felt reasonably certain they could defeat and look strong doing it. You could say that the Spanish American War served as the first step in the US rise to prominence, one that happened during the Great War. It couldn't be ignored anymore. This was the future for America that Roosevelt wanted. The right set of circumstances set him up to implement that vision.
So here, Roosevelt doesn't get his chance. He doesn't get attached to McKinley's ticket because he isn't a war hero. But all this does is delay American expansion and immersion into global politics. They're eventually going to see Japan rise to prominence after having been completely backwards just under 50 years prior. Or what's happening in China when the Europeans think there's weakness to exploit. Seeing Africa get carved up without themselves getting part of the action.
I'm suggesting that Spain crushes any revolts in Cuba thoroughly, all the while the Maine doesn't blow up to provide an excuse. The US is left looking longingly through the shop window while Spain manages to hold onto Cuba and Puerto Rico for the moment, but finds the Philippines succeed in gaining Independence, with Japanese assistance, bringing the Philippines into the Japanese sphere of influence.
The best the US can do is wait for unrest to flare up in the Caribbean, but without ever getting a "smoking gun" reason to intervene directly, they instead tacitly aid independence movements to succeed and gain independence from Spain around the time of the Mexican Revolution, creating a sphere of influence of it's own. I don't believe much of this will have too much effect on what's going on in Europe. Some form of the Balkan Wars will still break out and see the Ottoman Empire lose the rest of it's European territory. The Japanese still find a way to start a war with Russia to take Port Arthur, but instead of suffering a massive naval defeat like Tsushima, they manage to fend off the Japanese awhile longer, but are unable to hold onto Port Arthur. Russia is still defeated, but nowhere near to the levels of OTL's defeat to Russia, so thethe probl Russia encounters later on like the 1905 Revolutions is kicked down the can. This perception of Russia weakness isn't there to encourage Germany and Austria to careen to war with them, causing them to play a much more careful and deliberate game despite Wilhelm's best wishes. Italy won't leave the Triple Alliance. Meanwhile, with the loss of the Philippines in a long and bloody war, Spain decides to sell Guam, and sell it to Britain as a matter of convenience; Spain is loathe to see Japan gain Guam in the wake of them defeating Russia and assisting Filipino independence, while the British do not want to see Germany gain a useful territory in the Pacific. The US is never a consideration in this transaction.
1914 will come and go, seeing the competing armed camps or Europe staring each other down while a much more careful way of dealing with the Balkans while dealing with a Russia that isn't visibly close to the brink itself, and there is no war at this time. But no one is kidding themselves, a war is still a grim possibility. All the while, if there is still a Mexican Revolution of sorts that happens, the US, still a regional power with no real teeth in dealing with Europe, would likely involve itself more closely with the proceedings. Could a 2nd Mexican-American War flare up in full, especially if someone like Roosevelt is in office? Could the US see this a means to finally expand while Europe, still the center of world politics, is preoccupied with urgent European matters?