Here is everything that I learnt throughout this process:
I was not born a U.S. citizen, and I did not naturalise. Instead, I inherited U.S. citizenship at the moment I became an LPR (Legal Permanent Resident), because I both had a parent with citizenship and I was under the age of 18.
There is no paperwork to file to inherit citizenship this way, it is completely automatic and as a result there are people in the U.S. that do not know they are citizens. In order to assert that I was now a U.S. citizen, I just had to apply for either a U.S. passport, or a Certificate of Citizenship. There is no deadline to do this, because I was a fully-fledged citizen from the day of approval of my Permanent Residence application.
When I applied for my U.S. passport, I simply had to prove that I was a child at the time of receiving my Green Card, and that one parent was a U.S. citizen.
This is exactly what I had to provide the German consulate. I provided my own birth certificate, my I-485 form (with approval date) and my father's naturalisation certificate. Those were accepted without question.
To obtain a copy of my Form I-485, I had to file a FOIA request--I used a Form G-639 to make it easier--and I emailed it to [email protected].
I did attempt to get a copy of my passport application, as I filed that while under 18, but I was told by the State Department that they did not have a copy of it (curiously, several months later a full copy of my original passport application arrived by post from the State Department...). ThisThe response was not a surprise as when I applied for a passport at the age of 17, I was told by the official that they do not keep a record of my application, so I should also have a Passport Card in case my passport goes missing and I must prove citizenship.
Under German citizenship law, one loses citizenship when "voluntarily" obtaining another citizenship. The reason that I did not lose my citizenship when I became a U.S. citizen was because: I was a child, and it happened automatically. Therefore, it is not considered voluntary. Luckily, I did not have to explain this, since it was a consulate in the U.S. (Houston, TX) that I visited, they were well aware of the way in which I inherited U.S. citizenship. However, I had some trouble when dealing with the London embassy as they did not understand all of the U.S. citizenship qualifiers.
I hope this helps anyone else that finds themselves in a similar situation! I was completely lost when I started this process, but three months later I have my German passport in my hand.