What is used to initialise difference equations that require data from the output?
If there is no good reason to choose otherwise, you would initialize with zeros, so in your case $y[-1]=0$. Other initializations may be useful in certain situations, e.g., when processing blocks of data to avoid transients between blocks.

Note that if the filter is stable (which it has to be in almost all useful applications), the influence of the initial condition on the output becomes negligible after a while.