Moving Innodb database from Server A to server b Instead of using dump, is there a way I can move the data files from one server to another instead?

We are migrating our application to a new server in January, the one concern is the downtime when taking first server offline to do a dump of the database and the time to restore it on new sever.

I'm finding dump and restore is taking a long time due to size of database.

Thanks,
Jim

UPDATE:
Operating system is windows server
Old server is 5.5
New server is 8.0
Tables can be moved in physical form, although it is not instant: https://dev.mysql.com/doc/refman/5.7/en/innodb-table-import.html

A more automated way would to use partial or full backups with tools such as mysql enterprise backup or Percona XtraBackup: https://www.percona.com/software/mysql-database/percona-xtrabackup which will allow you to backup a database quickly without impacting sourde database availability.

In the future, having a replica of your database will be the easiest way to increase your availability during maintenance (switchovers should only take seconds).