What would American history have looked like if slaves were never brought over?
I will assume that you are referring to African slaves.
If no Africans were available, the British would have simply increased the supply of White convicts or Debtors in much the same way they used Convict labor and Debtors in Australia.
The likelihood is that the infrastructure of the United States agricultural and industrial is possible because of its incredible fast rise in the world this can be attributed to many sources but slaves are one of those as they replaced the weak and depleted native work force though not entirely damning to the future of the states having no slaves would have weakened the power of the US and likely would have changed it's ability to become what it is today
No slavery in the US? Hmmm...
I see cotton as the 600 pound gorilla of early American economics.
The enormous demand for labor to grow King Cotton would have to have been met somehow. I'm going to say that some sort of enticements would have been enacted to encourage more immigration of people willing to work the fields.
Perhaps similar to how the homestead act encouraged people to move west.
Whatever the poorest countries in Europe were (Ireland, Italy?) that's where they might be drawn from.
Maybe like Canada but mostly warmer? Could be worse. Also no neo-Confederates pissing in the water supply.