How do we know that Jesus was born to save His people?

In Matthew 1:21, the angel instructs Joseph, saying, 'Thou shalt call his name Jesus, for he shall save his people from their sins.' This verse encapsulates the purpose of Christ's incarnation, confirming that His mission was to save a specific group—His people, the elect—whom God the Father had given to Him. The clarity of this promise illustrates that salvation is not universally available in a potential sense but is effectively accomplished for those who believe according to God’s sovereign will.