So a PHP script is timing out (exceeds 30 seconds) while trying to restore the database? Is there any reason you can't use phpMyAdmin to directly IMPORT the backup (skipping the PHP script)? If it's the same version of phpBB that you're trying to restore to, you ought to be able to copy the files over and import (restore) the backup. If even that times out, you might have to break up the backup (.sql file) into several chunks, each with part of the tables. You also might have to contact support and get them to relax the timeout interval so the job can go through. They might have to do the restore for you, in that case. If the backup doesn't include commands to create the tables, you'll have to find out database schema is expected, and do something to create the empty tables. Finally, don't forget to update any configuration files in phpBB, for account name, site domain, changed directory structure, or whatever.
If phpBB's backup is not in standard .sql command format, but is some unique data collection, you may be out of luck (phpMyAdmin can't handle it). Maybe support can work with you to relax the time limit this one time.