Note that "Popular Sovereignty" means "people's rules", which is that the people hold the largest power, and that the government cannot be sustained without the people's support.
Note the Preamble:
"We the people of the United States, in order to form a more perfect union, establish justice, insure domestic tranquility, provide for the common defense, promote the general welfare, and secure the blessings of liberty to ourselves and our posterity, do ordain and establish this Constitution for the United States of America."
1) Inside, we can see that the first few words, "We the people of the United States" suggests that the Constitution was written by the people, for the people.
2) The next few lines suggest that through the people, the needs "perfect union,... justice..., [etc.]" are given to the people themselves, to ensure that the people would always have their rights (which would place them higher than the government.
3) Note the words "ordain and establish". By putting the Constitution as the highest law, it had garnered enough public votes to have it passed. This can be seen as one of the first examples of the Constitution already at work, and that it's content had already taken effect.
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