If you get full access to the CGA's registers (the 6845, mode control, color-select and status register), it should be quite straightforward to initialize the CGA card.
You can find the correct register values for each mode in the manual: minuszerodegrees.net/oa/OA%20-%20IBM%20 ... 0(CGA).pdf
Just write them to the card, and that's it.

The documentation I'm using says that the equivalent of "3D0/3D2/3D4/3D6" is available at "CF2C", the equivalent of "3D1/3D3/3D5/3D7" at "CF2D", to access the 6845; and "mode select (port 3D8)" at CF2E and "color select (port 3D9)" at CF2F, also providing a window to access the XT's memory. It also says:

C832: current CGA mode index, used by 6502 @ $6869 to setup 6845, or 6845 reg index
C833: 6845 data to write in the case where C832 is the reg index rather than a mode offset

(I assume "$6869" refers to an address in the program usually used to initialize the XT card.)

The software that initializes the card into booting DOS off a disk is definitely able to initialize the CGA itself, and displays a splash screen, I believe, from the 6502 side before activating the V30.

Keep in mind the usual rules for $C800 arbitration apply: you should access $CFFF to clear all cards from accessing it and then access $Cs00 where s is the slot number. At that point the $C800-$CFFE stuff for the PC Transporter is valid. Also, the Transporter's CGA is not quite standard: it programs 6845 settings which would cause extreme weirdness on a real card.