When I got my 7 day ban I tried family sharing but yeah..doesn't work
You can pick up a copy for quite cheap at G2A though if you're that desperate. Even if you do that you still have to get rank 3 which takes hours. Then you gotta play 10 competitive matches unranked (with a 21 hour cooldown after completing 2 matches) which will take about 5-6 days.
So you're better off waiting unless you want a permanent alt account in case you get banned again ^