Alright, then 
Be aware that a backup is not an export of the database and the restore of it won't take very long at all. In fact you could leverage existing backups and simply recover them.
Anyhow - your choice.
If you cannot follow this approach, all you can do is to perform a parallel export/import of the schemas you are actually interested in. Shouldn't be that difficult either.
Just as with the backup/restore approach you want to make sure that you perform the I/O operations against a mutually mounted/shared file system so that you spare the additional copy effort.
Finally the last option I see is to use SLT and perform an initial load - this won't be faster but you can avoid temporary disk usage altogether (if you already got a SLT instance in your landscape).
- Lars