You don't mention which architecture or version of tinycore you are using, but assuming tc-12.x x86, there are only the xf86-video-nouveau and xf86-video-nv drivers available.
As the name suggests, the firmware-nvidia extension contains only firmware.
There are various nvidia driver extensions in earlier versions of tinycore, but to use 12.x, you would need to manually install the required closed source driver unless your hardware works with xf86-video-nouveau or xf86-video-nv.