If you are looking for an eSIM with a German mobile number that does not require you to sign a postpaid mobile plan contract, there are not many options. While all three major German mobile networks and many MVNOs support eSIMs, they mostly only do so for postpaid plans.
Vodafone Germany only supports eSIMs for their postpaid contracts.
As a customer of o2 in Germany, you can also not get a prepaid eSIM.
Telekom does support eSIM for both postpaid and prepaid plans – you can find more information on the Telekom eSIM FAQ page. It is possible to order a new eSIM profile online and start using it right away.
Congstar also supports eSIMs for all plan payment possibilities just like their parent company – however, you cannot start using an eSIM immediately as it can only be activated by calling customer care. This requires possession of the physical SIM card.
Many Drillisch brands (smartmobil, yourfone, DeutschlandSIM, winSIM, …) offer eSIMs. Customers have to go through the SIM replacement process for their brand and pay the card replacement fee of currently 14.95€ to order an eSIM. It does not appear to be possible to start with an eSIM as a new customer.
simquadrat treats eSIMs as a first-class citizen and only offers prepaid plans. You can order an eSIM with a new German mobile number or port your existing one and get up and running quickly.