The Mass begins with the antiphons or opening hymn, not with the Sign of the Cross. Arriving at the door during the opening hymn doesn’t mean, “Shwew! We made it in time! They’re still singing!”
The opening hymn serves a couple of purposes. It is more than what a theme song is for a sit com. Firstly, it is meant to bring the community together. We have all come from our separate lives and (hopefully) just spend some time in private prayer preparing for Mass. The opening hymn is what initially draws us together in the same way that singing, “Happy Birthday” at a party or “Take Me Out to the Ballgame” at the 7th inning stretch or Christmas Carols at Christmas time.
Secondly it serves as the communities first opportunity to worship God as a corporate body. We are not just singing, we are worshipping - that is why not just any song will do! For those who don’t sing, they are missing out on worship. For those who hold back because they think they don’t have a good voice - God gave you that voice - give it back to Him!