The novelist's early manuscripts were rejected by every publisher she approached over nearly a decade. ______, her fourth published novel…

The passage describes a long period of rejection followed, after time passed, by eventual success, a straightforward temporal progression that eventually names directly. Conversely would frame the second sentence as a direct opposite or contrasting case, but the sentence describes a continuation of the same career over time, not a separate contrasting example. In other words signals a restatement, but success and rejection aren't the same idea restated. For instance would present the second sentence as an example of something just claimed, which doesn't fit this time-based progression.