No option. You can't do it. Physically it will take time to read the backup file and rewrite the disk. If you haven't pre-built the log file, that has to be zero'd out. If you don't have IFI enabled, the data file also has to be zero'd out. Both take time.

I don't know what your I/O subsystem can do, but 14TB is substantial. At the very least, I'd build a cheap, whitebox system that had consumer level drives of 16-20TB. That could probably be done for $2-3k these days and it would get you running quickly if you had some sort of log shipping enabled.