Do the teachings of Islam agree with what is mentioned in the Christian Bible (Romans 1:18-20) that nature points to God, and thus people have no excuse for not believing?

There should be no disagreement regarding the self-evident rational principles that indicate that an action implies an actor, and creation implies a Creator, and that inferring from the universe leads to the knowledge of the Creator's existence. However, the human intellect is limited in discerning the detailed way of life; therefore, it was necessary to send messengers and reveal books.

Indeed, Allah Almighty does not punish anyone except after the message has been conveyed and the proof established against them, as indicated by the sacred texts, such as His saying: (And We would not punish until We had sent a messenger.) Al-Isra/15. So, whoever the message has not reached at all will not be punished. And whoever the message reached generally, without detail, and proof was not established against them, will not be punished. As for whoever the call reached and understood the proof but did not believe in it, they are disbelievers who will abide eternally in the Fire of Hell.