Getting significant silicon fabricated is still outside of hobbyist territory. Programs like Tiny Tapeout exist, but the available area and feature size are not "build your own GPU" material.

https://efabless.com/tinytapeout

FPGAs are likely your best bet to start out, although large ones can still get very expensive very fast. You can start out by learning a design language (eg Verilog) and testing your designs in simulation without buying any hardware.