references for techniques to reduce recursive filter startup transients
For a given fequency response magnitude, a minimum phase filter implementation will have the shortest possible transient duration.

A minimum phase filter will have most of its energy packed at the beginning. Hence it's also called as a maximum energy filter. So it will produce steady state outputs as soon as possible (among the set of filters having the same frequency response magnitude)

However, a minimum phase filter cannot be linear phase simultaneously. Because linear phase filter would have a symmetric impulse response but that would also imply transfer function zeros outside of unit circle. Consequently it cannot be a minimum phase filter at the same time as for a minimum phase filter all the poles and zeros of transfer function are inside the unit circle. 

Alternatively, if you have some reliable estimation of the initial samples, before $n=0$,  of the input signal, then you can initialize the filter according to those values instead of a full blind zero initialization.