Copy a full backup to the new server, restore with no recovery. Then do a differential backup, copy to the new server can restore with recovery. Take notes on how long each step takes so when you're ready for the actual cutover you time time the beginning of the backup (or the transcontinental file copy) so that the differenital backup can correspond to the start of the scheduled downtime.

Or if the other suggestion of mrroring 2005 to 2012 won't work, but you have a suitable 2005 server & storage available at the US server, you can set up 2005 mirror at the US data center and make that the primary for the last day or so, and shorten the transfer time & uncertainty of a long-distance large file copy.