what is the fastest way to restore MySQL database without using dump files
Ofcourse a physical files restore will be quicker than loading a dump. So, if you have full physical backup / snapshot of mysql data-directory - you can go fast!
(Below answer assumes that you have physical backup available.)
Tables are MyISAM:

Stop mysql
Copy database folder to mysql datadir
Correct permissions
Start mysql

Tables are InnoDB:
If we have InnoDB tables in the picture then things are not as simple. Considering you have Xtrabackup.
You will have  to import tables one after another.
Refer Importing-Exporting-Tables-using-Xtrabackup OR how-to-recover-a-single-innodb-table-from-a-full-backup
(For this to work you should have used xtrabackup as backup option.)
Splitting mysqldump
If you want to extract only one database from full mysqldump then you might want to extract single database from mysqldump and load it (saves you from loading full dump).