All great literature is one of two stories; a man goes on a journey or a stranger comes to town. ~ Leo Tolstoy
American historical fiction is full of opportunities for stories of new beginnings. First you have the waves of immigrants from the Old World crossing to new beginnings in an entirely new land, and then the waves of settlers and adventurers setting out for new beginnings in the unsettled West. The reasons for both of these journeys were often similar—they were seeking better opportunities for making a living; they were fleeing from the law, from scandal, or from persecution; they were looking to start over after some financial disaster or personal tragedy. And all of this makes wonderful material for stories.
Years ago, traveling to a new country or even a different part of such a large and varied country as America often meant landing in the middle of an entirely new life. If a coming-of-age story deals with a character learning about life, then any story with a character making a new beginning is a coming-of-age story in a sense, because they're learning about a new life. It comes with so many built-in layers of conflict: their learning process and reactions to their new life; their attitude toward whatever they left behind and the reasons for their doing so. Personally, from reading a lot of book descriptions, I feel the plot about someone trying to escape a secret from their past has been overdone—but the new-beginning element doesn't have to be that complicated. It doesn't even necessarily have to be the whole story or the catalyst for the story; it could be more of an extra dimension to your setting. You could have a character who was born and bred in your particular setting, but then again you may want someone who's just discovering it all, with the reader seeing it for the first time through their eyes.
And, as Tolstoy pointed out, you can get a whole different story simply by flipping the perspective around. It may be your main character going onto a journey into a new land, or you could bring a stranger into a family or society who have already established themselves and formed an accustomed way of life in the new land. Either way, you have a story, whether the new beginning is a story in itself or just one element of the larger story.
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Image: 'Surveyor's Wagon in the Rockies' by Albert Bierstadt