It is impossible to read through the narrative of the birth of Christ without seeing it was intended for Jesus to be the savior of the whole world, not only the Jews. It is clear throughout the narrative that Jesus was going to be the Messiah, although many times it seems that he is only the savior for the Jews. Verses such as Luke 1:32-33, 46-55, 68-69, 71, 74, 77, 2:38, and Matthew 1:21-23, and 2:6 all point to a savior of the Jews coming to earth, and that Jesus was this savior.
However, it is also clear this salvation was not only for the Jews. In Luke 2:8-20, the angels announce the birth of Jesus, commenting in verses 10 and 11 that Jesus was/is a source of “great joy which shall be for all the people” for he was born “a Savior, who is Christ the Lord.” The angels then sing in verse 14, “Glory to God in the highest and on earth peace among men with whom He is pleased.” Coupled with the above verse we can see that Jesus would be peace for all who were saved. It is also telling, that peace with our fellow man follows after God is pleased and glorified.
Later, a man named Simeon tells of the salvation of the Gentiles through Jesus Christ, in Luke 2:29-32. This shows the salvation was not reserved for the Jews, but instead for all that would please God, which we find out later in the Gospels happens by trusting in Jesus as savior.