Is it permissible to debate with non-Muslims about matters of religion with the aim of convincing them to embrace Islam, especially if these discussions take place away from the public eye?

You must invite whomever you can to Islam, and explain the strength of the religion, its advantages, its suitability for humanity, and its solutions to humanity's problems, while emphasizing the obligation to follow it. This should be done with sound knowledge, evidence, wisdom, good admonition, and debating with disbelievers in the best manner. The methods of da'wah must adhere to the rulings of Sharia, so it is not permissible to be in seclusion with a non-Muslim woman. Caution should be exercised regarding establishing relationships with women. Inviting non-Muslim women should be done through Muslim women, or by a Muslim man presenting da'wah materials or public lectures without intentionally looking at women.