All can gain salvation through Jesus Christ. His bloodline is a sign. We needed to maintain awareness of the lineage until His birth & it is why it became possible to spread the good news to gentiles after He was born.
Perhaps. Or perhaps that bloodline and family affiliation business as a Jewish traditional cultural obsession into which God fit His Son in order to make an impression on the Jews using things he knew they would understand and value, as opposed to there being any intrinsic value in that bloodline.
I would go farther than you when you say "All can gain Salvation through Jesus Christ". I would say, to more perfectly fit the Gospel, that all who gain Salvation do so through Jesus Christ (although, to go a step further, it does not appear that all who gain Salvation REALIZE that it is Jesus Christ who is saving them until after they physically die). Enoch and Elijah, too, were saved by Jesus Christ, although they couldn't have heard of him until they were taken up into heaven, perhaps BY him, or perhaps by angels, etc.