I’ve received my frame and started the build. However, I’m having a lot of trouble with the internal routing. My specific question is whether I have to get the shifter cable housing inside the frame or not?
Yes, the shifter cable housing is internally routed in the frame.
You may be best served starting with the handlebar routing first, then routing through the headset and frame.
I did it the other way around, which equates to a lot of time faffing around with the handlebars.
Others may have better advice, but using inner cables as a guide worked really well for me
For the front derailleur, I would thread the cable through the shifters and housing once you’ve routed the housing through the handlebars and dry fitted the shifters
Then the inner cable can used as a guide to get the FD housing in position