Here is a plausible alternative scenario. As planets form, there is a certain window of opportunity where conditions are right for life to get going (among other extraordinarily unlikely accidents that must come together, the phase of planetary evolution must be just right). Almost always, this too fails. After all, every attempt to date to recreate primordial conditions in the laboratory have failed to produce any life.

I return to the key point: the number of planetary systems in our observable universe is not infinite. It is not much larger than atoms in a macroscopic chunk of matter. It is entirely possible that the probability of life forming on a given planet is much too small for it to have happened in the last 13.7 billion years. This is just like the fact that the probability of radioactive decay of an atom (even in a sizable sample) becomes unlikely if the half-life is too long compared with the time scale of observation.