SSD is not recognised with the internal SATA cable (13" 2010 MBP)
The actual problem here was that I installed the OS while the SSD was in an external enclosure, not installed in the internal bay. When I wiped the drive, installed it in the bay and then installed the OS from the old HDD, now in an external drive, my problems were solved.

I also tried another SATA cable before switching the positions, and that didn't help.