You can make a new partition (with a certain format, like NTFS) in Disc management, but indeed, it has to show there first. It's unclear why it doesn't, if the BIOS sees it.

Two questions:
- You're running Windows 10 from your current SSD and want to add a second one? Why that?
- Does GPARTED see it, if you boot from a Linux disc or stick (free to make)?