Could I convert my headset/handlebars to have internally routed cables?

I have a 2022 Giant TCR Advanced Pro 2 Compact: https://www.brickellbikes.com/products/tcr-advanced-disc-2-pro-compact. Forgive me, I don't know much about bicycle maintenance. The frame has internal cable routing, but I'd like to route the cables internally through my headset to my handlebars. Is this possible if I buy a new fork or handlebars, and if so, do you have any you'd recommend?