Do I have to finish babylon to join solomon raid?

Of course
You must finish babylon to unlock solomon

Naturally, yes.
Solomon is a singularity after Babylon.
Keep in mind that you also have to finish Babylon (it has to say "CLEAR" on the banner in Chaldea Gate) in order for you to quality for 30 Quartz Aniplex will give us, for the preparation for Solomon. You have about 6 days left for that as well (concluding December 20th).