SOLVED: This issue was due to having the SATA mode set to RAID in BIOS. It was resolved by first following this postthis post, then switching SATA mode to AHCI in BIOS and booting to Safe Mode in Windows which seems to install the AHCI driver needed to start Windows in AHCI mode.
After this, I was able to again restart from the elementary USB, choose "Try without installing" and starting the installer from the desktop. When arriving at the "Installation type" screen I was able to see the SSD, hooray! :)
However, after finishing the installer and rebooting it booted straight into Windows, bypassing GRUB - but that's a topic for another thread.
