Does Buddhism have a notion of providence leading unbelievers? Whenever an unbeliever starts inquiring regarding Buddhism or the Buddha's teaching, do Buddhists see this as providence leading the unbeliever to Buddha's faith or something else? Does Buddhism's notion of providence extend beyond karma?
Buddhists do not believe in a creator God nor in his or her divine providence. Buddhists believe in the law of cause and effect. When someone encounters the Buddhadharma it is because the causes of such a meeting are established and manifest.

There is no notion of divine providence and it is held that the law of karma is sufficient and necessary to explain how people encounter the Buddhadharma. Hope this answers your question.