FIR filter delay and window length
For causal FIR linear phase filters the delay you ask for can simply be computed from the group delay and is given by (for an odd length symmetric FIR filter of length $L=2M+1$)
$$\tau = - \frac{d\phi(\omega)}{d\omega} = - \frac{d-M\omega}{d\omega} = M $$

So it will shift every input component by $M$ samples at the output. 

NOTE: you can always produce your output sample $y[0]$ as soon as the first input sample $x[0]$ arrives. The delay is related with the information processing and not the sample processing;i.e., your initial $M-1$ output samples will be called as the filter transient response, before the steady output is computed.