The idiom "RAY of hope" means something that gives one respite or happiness and optimism especially after having experienced some bad times that seemed overwhelming.
The letter "R" is most definitely the right letter to complete the gap to form the appropriate word "RAY", which when paired with the words "of hope" gives us an idiom that perfectly goes in agreement with the whole idea of the message the sentence conveys.
The most appropriate word is definitely "RAY". The birth of a child is what is likened to a "ray of hope" in the given sentence. This gives hope and optimism, as posited by the author.
