The question title says it all, really. I upgraded my SSD and now I don't have a disk to boot from except OS X Recovery. I have both Internet connection and a USB drive from which I can install a clean copy but I would prefer not doing so unless it is necessary because that usually takes a lot of time. When I try restoring from a Time Machine backup it says "Searching for Time Machine backups..." although my backup drive is connected.
Yes, it's possible via recovery (Hold during startup ⌘ Command R). If you can't find a Time Machine backup in recovery, try holding ⌥ Option during startup and after that choose Time Machine drive.