I'm not sure what the criteria is for receiving the $300 credit. Since there was nothing in the setup instructions about it, I assumed it was automatic for new Google Cloud instances. However, after day 1 of contributing (an impressive ~20k games, I'll add) under the "Billing" link, my account shows:
Cost before credit: 8.99
Credit: 0.00
Cost after credit: 8.99
If anyone has ideas of how I might have missed out on the credit (or ways I might still be able to receive it), please let me know. Until then, I'll be shutting down my $270/month instance.
For anyone else who just followed the Google Cloud instructions in a "set it and forget it" mode, I encourage you to circle back and double-check that the $300 credit was, indeed, applied to your account. Not checking could prove to be a costly mistake!