The English word Adoption is found five times in the New Testament in Romans 8:15, 8:23, 9:4, Galatians 4:5 and Ephesians 1:5. However the Greek word for adoption is not in the New Testament.
What is found is a word that means “placement of sons”. That is placement of those who are already sons. The idea has to do with coming of age. The word was used to denote one who was ready to inherit what he was already due to receive. He was a natural born son.
The use of the English word adoption is misleading. It is not about other people who are not natural genetic sons becoming sons. Romans 9:4 can not be spiritualized.
Romans 9:4 “those who are Israelites, whose is the position of sons, and the honor, and the covenants, and the legislation, and the service, and the promises”.