Can I apply for a master's without waiting for my certificates?

At some universities, yes — but there is no Germany-wide rule; each university and programme decides. Whether you can apply before holding your degree certificate or language certificate depends entirely on the programme you choose.

#No degree certificate yet

• The university decides whether it accepts a transcript or a certificate of expected graduation at the application stage. Check the programme's application page.
• For master admission the university checks your bachelor's subject fit, grade, language proof and documents individually. There is no national GPA, NC or language threshold.

#No language certificate yet

• The required proof and level vary: German-taught programmes often ask for DSH or TestDaF, English-taught ones for proof such as IELTS or TOEFL. There is no universal C1 or B2 rule.
• If a programme offers conditional admission, it is tied to the condition the university sets, and that university's rules decide what you must submit and by when.

#What to do

• Read each programme's requirements and deadline separately — there is no single deadline that applies to everyone.
• If the programme uses uni-assist, the uni-assist deadline is the university's deadline.
• When in doubt, ask the admissions office whether documents can be submitted later.

Source: Conditional admission and language level guide · DAAD Admission Database