This is demonstrated when Jefferson had his realist instinct of knowing the strategic importance of New Orleans that led to the Louisiana purchase. Other examples include: carrying out the manifest destiny, admitting Texas into the union in 1845, the war of 1812, and the US-Mexican war; all for the aim of continental expansion and a rapid expansion of industrial and regional power. The US now had secure borders and a great geographical advantage compared to other countries that help put them in the hegemonic position they are in today. .
To be clear, I am not claiming that the US has predominately exhibited strictly offensive realist tendencies. It most certainly has implemented the use of liberalist ones, especially when it comes to overseas expansion and the rapid expansion of the United States' foreign policy. The contemporary US does, and has in the past, utilized liberalist tendencies to do things in foreign policy like promote democracy, alliances, extend commerce, etc. because it was founded on freedom and liberty. The United States is considered the liberal country by other countries worldwide. But, the underlining motive is almost always of realist tendencies, even when the US does exhibit liberalism. The key defining factor that compels the offensive realist argument over the liberalism one is the method of expansion and hegemonic stability that the US has and continues to utilize now. .
Using WWI as an example of when the US tried to implement strictly liberalist tendencies and how it failed: when idealist, Woodrow Wilson claimed that the war was good for democracy, would expand markets, and build allies. That was all true and beneficial to the US, but it did not work after the war when Wilson and other idealists placed their hopes for peace in the League of Nations as a formal structure for the community of nations as it was soon to be proven helpless at the start of WWII.