I'm not an immigration lawyer, but my understanding is that you can not go from Student Visa to Green Card or H1B or whatever without returning to your home country unless there are specific extenuating circumstances.
I don't believe this is totally correct but I'm not an immigration attorney or expert either. I don't necessarily believe one has to return to their home country to initiate the process as long as they have lined up a visa-sponsored job upon the conclusion of the student visa. In many cases the student may not even get any chance to go back to the home country, and if allowed once their employment starts, such visits might be limited in number and for short duration.
An international student has to be able to secure employment allowing them to go from a student visa to a work visa/H1B (probably within a 60? day window of graduating), which visa has to be continuously sponsored by an employer. Maybe the NBA or its business entity that runs the G-League could be an example of an employer-sponsor in the case of a professional basketball player.
With a work/H1B visa (which probably needs to be renewed every X years or so) in hand, you start the citizenship process by applying for a green card/permanent resident status.
Once you are granted a green card (this could take a few years) recognizing you as a permament resident of the U.S., you then apply for full citizenship which historically would be a 5 years or so waiting period that has also been known to drag out to 10 years or more.
During this entire combined period of holding a work visa followed by holding a green card, I believe you can't really leave the U.S. for an extended period as you demonstrate your desire to make this country your home. Not sure how playing overseas basketball seasons in Europe/Asia every year would be viewed by immigration officials but suppose it might be kosher if you keep coming back to U.S. during each off-season.