Different ways to log in to MariaDB
Yes, there are several ways to authenticate, but you have to specify this per database user. Before MariaDB 10.4 each user could only use one authentication method. You can change the authentication method for a user if you can log in as the root or other sufficiently privileged user. Use the ALTER USER statement if you're on MariaDB 10.2+, otherwise use UPDATE mysql.user SET plugin = '...' WHERE user = 'the_user' AND host = 'the_host';. 

Authentication is done by authentication plugins. Run e.g. this to see which plugins you currently use for your database users:

SELECT user, host, plugin FROM mysql.user;


Some common authentication plugins are mysql_native_password and unix_socket. The former requires a password and works over TCP whereas the latter works over the MariaDB socket file (by default it's at /var/lib/mysql/mysql.sock in Linux) and doesn't require a password, but it assumes your OS user has the same name as your database user, and obviously only works if you're on the same host as the MariaDB server. Perhaps this is something you could try to avoid SSL?

Relevant MariaDB Knowledgebase documentation


ALTER USER - authentication options
Pluggable Authentication Overview
Authentication Plugin - Unix Socket
Authentication from MariaDB 10.4