Everything that we love about America was born from Christianity. Everything.
What about Bald Eagles? I am pretty sure that eagles - let alone this specific species from across the ocean - they have next to no Biblical significance - the only one I can think of being as a symbol of John the Evangelist (…and, as it turns out, the evangelists’ animal iconography seem to have Babylonian roots…). No, the eagles’ worldwide prestige comes from the eagles themselves - of all the birds that freely roam the skies to the envy of us earthbound ground-apes, the eagle is the mightiest and most majestic. And of course, such a “king of the skies” makes for an obvious pick for an animal to associate with a god ruling over the all important weather. The eagle iconography in particular is deliberately tying back to Ancient Rome and the Hellenistic world - that considerably predates and indeed was what gave birth to Christianity (especially post-Pauline, post-Flavian Diaspora, non-Nestorian, non-Oriental-Orthodox Christianity, i.e. the vast majority and everything European) -, adapted to use the strikingly coloured eagle of their new land.
Asides:
1. The “bald” in bald eagle preserves an archaic meaning of the word - white-haired.
2. Sea eagles, such as the bald eagle, are not actually true eagles but rather more closely related to certain kites. (Still better than falcons turning out to be completely separate from the other diurnal raptors, all the while being the eponym of the taxon (the hawks have taken on that role for what remains. Alas, Accipitriformes deoes not roll as gracefully as Falconiformes. And in another plot twist, the New World vultures turned out to be the sister group of the hawk-kin after all, rather than relatives of storks, although their resemblence to Old World vultures is still convergent evolution.)
You don't have America. You don't have Europe. You don't have Western civilization without Christianity. It would be unrecognizable without it.
It is true that Christianity has been a major force in basically all European cultures, including colonial ones, for a very long time now. But they certainly cannot be reduced to it at all. And humanism, too, has been an incredibly important element of Western European culture - especially the founding of the United States! - for many centuries, including in regards to the interpretation of Christianity.