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.
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.
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.