I've been playing with the idea of making a handheld TIC-80 console (similar to a Gameboy Original) with a raspberry pi, and pre-install all of the best games from the website, but it would have to go straight to surf mode because there'd be no keyboard. 

Any ideas how something like this could be done?

The best solution would be adding such an option to TIC-80, but for now you can use xdotool (https://www.semicomplete.com/projects/xdotool/) like this:

tic80pro &  # Run TIC-80 in the background. Change `tic80pro` to whatever your binary is named, of course
sleep 3  # Wait for it to start. On a RPi this number might be higher
xdotool type --delay 99ms surf  # Type ‘surf’ but not too fast. Again, tweak this number so it works
xdotool key --delay 99ms Return  # Hit the return key