After reviewing almost every narration in the books of seera, I can't find any examples.
I can only conclude the Prophet (saw) did not proactively call non-influential individuals to Islam, as is often imagined with protestant missionaries call individuals to their faith.
Most converts to Islam, ranging from Abu Bakr, Dawud al-Tausi to Abu Dharr al-Ghaffari, Amr ibn Abbasah and Bilal, heard rumours of his discussions with tribal leaders requesting they reorient society to a new worldview based on the divine. He critiqued fundamental polytheistic values and beliefs of Meccan society, ancestralism and socio-economic practices.
Those approaching the Prophet (saw) would be told of his message, the revelation he had received and the truth. Those who believed him would tell others and bring them to the Prophet (saw).
This does not mean the prophet (saw) neglected or rejected non-influential individuals who accepted the truth of his message; rather his approach was to win over the influentials and elites of society, who could more readily ensure a transition for all of their followers.
Where individuals approached him, he responded to them, answered their questions and spent time teaching them and helping them build their personalities. After it became clear the Quraysh elites would not entertain the prophet's call, he spent increasing amounts of time with the companions in Dar al-Arqam, preparing them for the next phase of the dawa.
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