Lucups, Floris is right, but you comment that this didn't solve your problem. I ran into the same symptoms, where mysql (mariadb) will not accept the blank password it should accept, and '/var/lib/mysql' does not exist.
I found that this Moonpoint.com page was on-point. Perhaps, like me, you tried to start the mysqld service instead of the mariadb service. Try:
systemctl start mariadb.service
systemctl status mysqld service
Followed by the usual:
mysql_secure_installation