I started making mods for doom 2, then duke3d and people liked them so I made a partial conversion for Doom2 that added new enemies, behaviors, sounds, several levels. I recruited some help but and it took a year, but it covered all the major aspects of making a game at the time. It won some awards and I loved doing it, so I risked the family business and borrowed millions of dollars to make Gore in 98.
Gore took 5 years, and sold a decent amount of copies, but the publisher didn't want to invest in a sequel and took the money and ran. We were out of credit at the bank and the royalty advance they gave us wasn't enough to keep going. We scored a crappy deal with Activision that kept us going until 2004 when we went out of business and I went back to fixing cars for a year. (insert sad meme here) Rick moved and got work in the industry. In 2005 I got a small deal to make Patriots and gave up car repair for good. After Patriots was finished I worked for NC Soft on Dungeon Runners a goofy MMO that got cancelled in 2008. At that time I got into real estate and invested all my cash into it.
For the next several years I acquired more rental properties and built up sweat equity. By day I fixed up old foreclosed houses and rented them out, at night I worked on Oblivion mods and improved my game design chops. Those got a lot of attention and downloads and pacified my creative desires and iterating live (like the EA model we have now) on my mods allowed me to take a decent idea and hone into a masterpiece. It was also good networking, one of the guys I worked with ended up investing into my real estate business allowing me to expand faster. The other guy went on to work at Obsidian, and probably worked on Outer Worlds.
Come late 2012 I became a paper millionaire and had enough cash flow to live on and wanted to get back into the game industry making my own games, and that famous Thanksgiving transpired that gave birth to the idea of 7 days to die, a survival horror game that would blend elements of Minecraft, Fallout, and The Walking Dead tv show.
So in a nutshell, start making mods, network with people and believe in yourself. Its 1000x easier today with early access and people willing to put their credit card into a computer and download digital games. Back in the day you were at the mercy of publishers to get your product out there and you built 80-90% of the game on your own, then got some funding and got robbed to bring your game to the market. Now you can build a small demo, go to EA, and make a fortune if your game is fun and it stands out in the crowd.
There are also game schools where you can learn and they have pretty good job placement. So its easier to get in now too. Either way its work and learn during your spare time and build a resume.