The PHP execution time limit cannot be increased on free hosting. The ability to customize those limits is a feature that’s only available on premium hosting.
We also recommend against using backup and migration plugins. The backup process itself generates very high server usage which frequently cause account suspensions (notably IO suspensions). And due to the limits set on free hosting, restoring these backups generally doesn’t complete successfully, leaving you with a backup you can’t use.
So how do you move your website instead? Simple: by following the procedure recommended both by us and by WordPress.