how do you get a career as a coach or in the front office of a professional sports team?

Word hard. Work while others are resting. Work when you want to rest. It's not impossible, but also not easy. NBA teams hire lots of interns each season so that is a good way to get your foot in the door a la Eric Spoelstra. Research his story if you don't already know it; while it is the exception to the mean, it doesn't mean you can't replicate it yourself.

Additionally, understand the sport management is a business just like everything else. The least tolerated thing for working in sports is fans masquerading as professionals; work hard, but also be cognizant that players, coaches, team staff, etc., are fans second and professionals first. Working directly with players is cool, but don't let it blind you from your goals and the culture of the industry.

It is basically impossible and shouldn't be anyone's goal. Getting any kind of job in professional sports is a million to one longshot.

Coaches are generally people who played professional basketball at some level (development leagues, Europe, NBA), even if not for very long. They used that opportunity to build their contacts and learn about the game at a professional level. Front office types generally follow the same path, or have business or marketing skills AND somehow made contacts in the pro sports scene.

Pretty much the only other path is to be the absolute best at every non-pro level coaching job and rise up the ranks that way. Eg you dominate your youth league so you get offered a job as a highschool coach. You dominate your highschool league and go do a NCAA D3 school... rinse, repeat, until you are a top-5 NCAA D1 coach whose team does well in the NCAA tournament... THEN an NBA team might hire you.