The phrase "after I first got" is correct and usable in written English.
It can be used to indicate a point in time following an initial acquisition or experience.
Example: "After I first got my driver's license, I felt a sense of freedom I had never experienced before."
Alternatives: "after I initially received" or "after I first obtained".
"When I'd go visit the family after I first got here, he'd talk instead about his work with Carla Bley.
For two or three years after I first got demobbed, I don't think I would have minded whether I lived or died.
"After I first got it done, I wasn't interested at all in getting a boner.
But the context is that Google Glass is a deeply flawed product and I expected a LOT more improvements by now, 11 months after I first got mine.
Less than two years after I first got hooked on those magical two minutes at the end of that Headbangers Ball tape, Soundgarden exploded into the mainstream with their 1991 album, Badmotorfinger, alongside Nirvana, Pearl Jam, and Alice in Chains as part of the Seattle grunge scene.
In January 2010, shortly after its unveiling, I first got my hands on an iPad.
I've played a good few matches of the Pro Evo 2016 demo now, which features a handful of club teams alongside the French and Brazilian national squads, and I still feel the way I did after first getting my hands on Konami's FIFA-challenging football sim at this year's Gamescom: maybe, just maybe, EA's license-magnet might find itself the second-best soccer game of 2015.
One particular experience that stuck with me came right after I got third place in a national championship race in Indianapolis.
"After I got that first out in the seventh, I was just hoping I didn't go down with something," Hughes said.
"And like [Rob], I never felt good about going, 'Hey Mommy, can I have some money?' After I got my first paycheck at Taco Bell earning $4.25 an hour, which was minimum wage at the time; I thought I was the man.
After I got the first one, I laughed.
