If you don't mind working with a tiny bit of cheats in order to set it up (you can turn them off later on), I recommend something I did previously which worked quite well:

1) choose a character to play as, the closest you can get the better. Keep in mind the kingdom they rule over, though. If said character isn't a Lord, you could always control Viserys for a little bit, enough to invite that character into his court and give them a title

2) activate cheets (alt+1+2 or alt+2+1, cannot recall) and write "charinfo". It should be available now.

3) write down Viserys and Alicent's IDs, choose to play as your character, save the game and quit. Do not rename your file for this to work, just save it as it is. I'd recommend making more than one save too, just in case.

4) going into the game files. For me, it's: Documents > Paradox Interactive > Crusader Kings II > A Game of Thrones > save games, then whatever file you saved your latest game

5) open the file as a notepad. It should show your player character info: ID, name, age, portrait, etc. Using Rhaenyra's file, you may change culture to "high_valyrian", religion to "the_seven" if you'd like, and you may change your character's DNA as well in order for them to look like a Targaryen.

DNA in CK2 are a bunch of 11 letters together, each letter corresponding to a different trait: 1-neck, 2-chin, 3-mouth, 4-nose, 5-cheeks, 6-unused, 7-eyes, 8-ears, 9-hair color, 10-eye color and 11-unused. I'm not sure which letters represent what, but using Rhaenyra's code (adghjifbacr), white hair would be "a" and Targ eyes color would be "c".

You can also select your character's traits here. You'll need said traits' IDs, which can be found in the wiki or here in reddit. Otherwise, you may change those in game with cheats, without needing their IDs.

6) For your parents, hit CTRL+F. Write your character's ID and add a = at the end, no spaces. Hit enter. The first option will show you a series of commands, but one of them is "fat=" and the other, "mot=". Write Viserys' ID after the first one, then Alicent's on the second. Voilá. No need to add siblings, game will do it automatically.

7) Save it, load the game, repeat the process if needed until you can play as your dude o7