After a clean install of mySQL or MariaDB on Docker, you should be able to connect to the database as root on the Docker system. The docker exec command with the -it or --interactive --tty files can be used to get a shell on the container.
docker exec -it mariadb bash
You should be able to connect to MariaDB as root, using the password that you defined in the MARIADB_ROOT_PASSWORD variable.
root@c132e43cd93a:/# mysql -u root -p Enter password: Welcome to the MariaDB monitor. Commands end with ; or \g. Your MariaDB connection id is 3 Server version: 10.6.4-MariaDB-1:10.6.4+maria~focal mariadb.org binary distribution Copyright (c) 2000, 2018, Oracle, MariaDB Corporation Ab and others. Type 'help;' or '\h' for help. Type '\c' to clear the current input statement. MariaDB [(none)]>
To be able to make a remote connection to the container, the /etc/mysql/mariadb.conf.d/50-server.conf file in the container will need to have the bind address of the container. For this reason, you may want to use the docker cp command to copy the files in the /etc/mysql/mariadb.conf.d directory in the container to a directory on your Docker system, such as /usr/local/docker/mariadb/mariadb.conf.d.
docker cp mariadb:/etc/mysql/mariadb.conf.d /usr/local/docker/mariadb
Then edit the 50-server.conf file to have the IP address 0.0.0.0 so that all connections are allowed. Or, this could instead have the IP address of the container.
bind-address = 0.0.0.0
You would then use the --volume option to mount /usr/local/docker/mariadb/mariadb.conf.d directory on your Docker system to /etc/mysql/mariadb.conf.d in the container, and also use the --ip option to assign an IP address to the container.
docker run --detach --publish 3306:3306 --volume /usr/local/docker/mariadb/root:/root --volume /usr/local/docker/mariadb/mariadb.conf.d:/etc/mysql/mariadb.conf.d --ip 172.16.0.2 --env MARIADB_ROOT_PASSWORD=itsasecret --name mariadb --restart unless-stopped mariadb