On September 3 of 1902, President Roosevelt dies in a tragic accident when a trolley slams into his carriage. Without a Vice President, Secretary of State John Hay is elevated to the Presidency. A close ally of the late President, Hay appointed Governor of the Philippines Taft to replace him at State. Taft begrudgingly accepted.
Feeling aged, President Hay was initially reluctant to run for another term in 1904, but changed his mind to help resolve the deadlocked convention in Chicago. Taft was drafted against his will and Vice President Hay's front-porch campaign has a relatively easy time defeating the Democrats, who again nominated the progressive but divisive William Jennings Bryan. Hay, however, was plagued by heart conditions and was sickly during his inauguration on March 4, 1905. President Hay died July 1, 1905. Taft, the reluctant President, had already been involved in many executive duties. His immediate focus on the Russo-Japanese War would result in the Treaty of Portsmouth and lead to him winning the Nobel Peace Prize.
There's a start. He could proceed with the progressive, domestic reforms that Roosevelt and Wilson did IOTL. Re-elected in 1908 over a conservative Democrat by 1912 he is popular enough to run again in 1912 with the "two election" pledge.