Not all meteors occur due to the Earth’s passage through a debris field left behind by a comet. While there is a definite increase in the chance of observing shooting stars on nights when the Earth is indeed hurtling through such regions with increased counts of small rock fragments, sporadic meteors occur all the time.
While their origin is in many cases uncertain, such sporadic meteors do not all originate from any particular radiant. In other words, it is indeed oftentimes possible to observe shooting stars on any given night, provided good weather and low levels of light pollution, ideally during the new moon phase.