This statement is true. There are several different events that show America is far from isolationist during this roughly 160 year period. Here are some examples of major events that show America's lack of isolationism.
1) Manifest Destiny- During this era in American history (early to mid 19th century), the US gained thousands of miles in territory from countries like France (through the Louisiana Purchase) and Mexico (through the Mexican-American War and Mexican Cession).
2) Imperialism- The era of American imperialism (late 19th and early 20th century) resulted in the US expanding their territory, annexing places like Puerto Rico and Hawaii.
3) World War I (1917-1919)- The US got involved in World War I after Germany made several actions that upset the American government and citizens. This includes the sinking of the Lusitania and the Zimmerman Telegram.
