Migration of MariaDB/MySQL to another server without downtime
Are you using LVM on Linux servers? In that case, you can have a minimal downtime solution:

Switch the database to master, stop the server just a few seconds to make a LVM snapshot, start the master again, mount the snapshot in a temp directory to copy the data to the new (bigger) server and then configure a slave with that. Then you can start the slave, let it sync with the master until is up to date and finally promote the slave as master.

Detailed howto: https://www.percona.com/blog/2006/08/21/using-lvm-for-mysql-backup-and-replication-setup/