Welcome to our community and thank you for your question.
In general, it's crucial to have a valid passport in order to marry. Maybe you can get in contact with Standesamt, tell them about your situation and try to find out whether there is another way to prove your identity. Maybe an expired passport or another document will do. Some Standesämter might be more accommodating than others and allow a marriage under these circumstances. Otherwise I don't really see a way how you can get married.