"The US" doesn't really exist. What has existed are a bunch of people who made various compacts about how things should work. As such, "the US" didn't set out to be anything. A bunch of people had some ideas, often at odds with each other, and reached various compromises to create compacts around an idea called "the United States". Then they died, and their children, with their own ideas, often at odds with each other, reached various compromises, modifying these compacts. This chain of generations has gone on for a couple centuries, until those of us who are residents of the United States, each with our own ideas, reach compromises with each other around those compacts called "the United States".
All countries are like this.
Our ancestors would be amazed at some of what we've done, horrified at some of what we've done and smugly satisfied at some of what we've done.
Some of what our decendents will do would amaze us. Some of it would horrify us. Some of it would leave us smugly satisfied.
To be more specific: Some of the founding fathers very much wanted to abolish slavery. Others did not. It took nearly a century to work that out.
With regards to "manifest destiny": some people very much believed in it. Others were very much opposed.
With regard to trade with Britain: some people wanted to align with Britain almost immediately. Others wanted to align with France. This was actually one of the core conflicts that drove the creation of the first parties.
Countries don't "set out" to do anything, even those founded, at least in theory, on philosophical principals.