Dual citizenship

You have to renounce your other ctizenship when you receive the German one.

Except in very narrowly defined special cases, double citizenship is not allowed.

And, to become German citizen, several years of living here is required (and your prior stays at birth and in the 70ies do not count).

I have to add a lot to what Beppi wrote. It is true as a general rule that if one has a non-EU citizenship they have to renounce to naturalize as German. Lots of exceptions though.  Some countries, like Argentina, don’t allow renunciation and Germany allows their citizens to naturalize without giving the previous citizenship up. Also citizens of countries at war or severe civil unrest like Yemen, Syria., Afghanistan etc. are presently exempted but the list varies over time.  Even as a US citizen, I qualified a few years back to naturalize without renunciation. This was an economic hardship case; if the renunciation fee exceeds the average monthly income over the previous year to applying one is exempt. But if one earns too little then they won’t qualify to begin with.

The other thing is that present “traffic light” coalition government has proposed a radical overhaul of immigration rules. The claimed purpose is to encourage immigration of highly skilled workers that are in demand. From what I understand it is a done deal but won’t be implemented until 2024; getting rid all restrictions to multiple citizenship. No renunciations will be required. One just needs to wait a bit until this law goes into effect. But of course they must still meet the many requirements for naturalization. 

But the OP seems to have an interesting situation. Born in Germany to German parents from what I understand; they should have been German by birth. The parents migrated to the US and would have lost German citizenship upon naturalizing in the USA. But if a child is also naturalized, I’m not positive that their German citizenship would have been withdrawn. Such a procedure that occurred as a child is beyond their choice and control and capacity as a minor to understand. They might well have legal grounds to challenge the loss of citizenship if this indeed was the way it happened.  Otherwise, as Beppi mentioned, the process to naturalize takes years. For most people unless married to a German spouse the current requirement is 8 years of residency. But this is to be shortened to 5 under the new rules. Still a while to wait for someone who is 72.