They did. If you look at the American territories throughout the world that are not contiguous to the US itself, it can be seen that America did and does indeed have an empire. Territories like Hawaii, although now a state, were seized from their native rulers by military force, or the threat of it, and certainly did not become American by the permission or request of the native population, who simply weren't consulted. Other non-contiguous territories like Alaska became American by purchase, but again without the native peoples being consulted. Puerto Rico was taken from Spain, again without the native peoples being involved. So, by any definition, the US had, and still has, an Empire.