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There are at least ATMs at the airport where you can get cash payouts in US$ and I am relatively sure that ReiseBank has an ATM at the main railway station, also able to give you US$ notes.
I would however not assume that this is the cheapest solution. German ATM operators notoriously hide all kind of strange fees and I would expect that if you try to make a US$ payout on a German ATM from a UK card, the ATM operator will convert the amount in US$ to EUR at a poor exchange rate and then charge your card in EUR and not directly in US$.
Currency exchange in regular banks is often only provided to the bank's customers and is also usually quite expensive. The most prominent exchange offices, e.g. Western Union or ReiseBank neither provide very good exchange rates. I would assume that the best solution is to get EUR with your card from an ATM and then go to any of the smaller, independent exchange offices. Many of them are located in the area south of the main railway station between BayerstraΓe and Schwanthaler StraΓe.