1901: William McKinley shot, Roosevelt takes control.
1904: Popular Roosevelt Re-elected.
1908: Roosevelt runs for third term
1912: Republicans refuse to back Roosevelt for fourth term. Roosevelt beats Wilson and Taft as Progressive.
1914: Archduke Franz Ferdinand of Austria-Hungary assassinated, The Great War begins, Roosevelt support British.
1915: TR starts to build up the Army and Navy. After the Luitania is sunk TR sends the Navy in to the North Sea and Eastern Atlanic. Germany stops unrestricted submarine warfare.
1916: TR lays down his three points for peace.
Point 1: Borders go back to pre1914 lines.
Point 2: Noone is blame for the start of the war.
Point 3: They form something close to the UN and not the League of Nations
Russia, UK, France, Italy, and Austria-Hungary agrees but not Germany. Because of the American Navy being in the North Sea Germany loses a large number of her navy in the Battle of Jutland. Germany starts unresticted submarine warfare again. With in weeks 5 american ships are sunk, america goes to war with the central powers.
1917:Because of the large numbers of american troops germany start to fall back on the western front. The german reichstag overthrow the military wing and agrees to TR three points of peace. Lenin never gets to russia and the russian revolution is a more even fight. The western allies send troops to aid Russian Empire.
1918:A fair peace treaty is work out at Versailles. With allied support Nicholas II stays in power. In Germany Wilhelm the second step down and germany becomes a republic under Paul von Hindenburg. Germany starts down the road to becoming a strong democracy.
1919: TR attack Mexico because of the Pancho Vila Raid into SW America.
1920: Mexico surrenders to america and TR takes over Baja and other northern mexican states.
1921: TR does not run for six terms. He supports Hiram Johnson for Presdent. Wilson loses for a thrid time.
In this timeline there would have been no Second World War in Europe or Soviet Union. Japan would had still attack America and the other western allies but because there was no war in Euopre japan would have been lose only are two or three years of war.