"A poco" at the beginning of a sentence

"A poco, William Doe comenzó a hacer la corte a Jane, con éxito."

This is from a newspaper article from the 1900s.

What does "a poco" mean in English in this context???? I'm sorry I can't find any resources on this.

Does it translate to, "Before long, William Doe began to court Jane, with success?" Or "Gradually, William Doe began to court Jane, with success?", Or "Shortly, William Doe began to court Jane, with success." ???

Sorry for the dumb question but I'm really stuck here 🙁

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