The definition for the term "green thumb" is; one who has an exceptional ability for the cultivation or care of plants.
Adding potting soil or a better quality soil to existing soil is one simple way to help plants grow. Seeds germinate more efficiently in better quality soil due to nutrients and moister. Soils can also carry seed even if you don't see them. Seeds naturally spread in many different ways. Animals, air currents, and running water all can carry seeds to new homes. My family has raised turtles in our backyard and they love tomatoes. One year I had tomato plants popping up all over the yard and in all the flower beds because the seeds do not break down inside the turtles. The turtles simply pass the seeds through their digestive systems and then deposit the seeds in new locations.