His parents, Frank and Lynne, were supportive, but wanted him to get his college degree, recognizing the uncertain nature of professional sports.
Excited to start his pro career, the defenseman assured his parents he would finish his education at some point.
Ten years after signing his first contract with the Kings, and 13 years since he stepped foot on the Oxford, Ohio campus, 30-year-old Martinez made good on his pledge.
"Lots of people go to school for 13 years," Martinez said, pausing for dramatic effect. "They're called doctors."
Lynne said, "For me, the best thing is he followed through on his promise. That really impressed me. You tell somebody you're going to do something, you better do it. That's how we raised him."
It was a long and winding journey, seemingly forgotten during the Kings' Stanley Cup championship runs in 2012 and 2014, as well as his injury rehabilitation periods.
It was also a secret. Alec was studying and taking tests on the sly, his parents completely in the dark.
"These past two and a half years, he's been taking classes and we didn't have a clue," Frank said.
Martinez used humor to deflect years of mostly gentle queries from his parents about the degree. They teased him that his younger sister Maria, 24, had her undergraduate degree and a master's in journalism.
At first, Alec went back to the Miami campus to take classes but it became more difficult when the Kings had deep Stanley Cup Playoff runs.
So he finished his studies online. The key was keeping his pursuit a secret from his parents, wanting to surprise them.
The payoff finally came this Thanksgiving when he gave them the gift of a lifetime.
Frank and Lynne were in Hermosa Beach, California, for the holiday and weren't sure what to think when Alec stood up to speak to the family. It reminded them of his Stanley Cup celebratory parties when he made a point of thanking everyone for their support.
Martinez scored the Stanley Cup-clinching goal against the New York Rangers in 2014, an ecstatic moment forever etched in the memory of every Kings fan and his family and friends.
Of course, that moment was wildly unexpected, coming in double overtime in Game 5.
So was this.
"I didn't know what he was going to say," Lynne said. "He thanked everyone for coming. I knew it was serious. He had a piece of paper where he made a pseudo diploma that said he was graduated. He really hadn't graduated yet because he had to take his final.
"I was overjoyed. I told him not to buy me a Christmas present because that was present enough. We were just thrilled because we had wanted him to do this."
Martinez put the "diploma" in a shoebox and wrapped it, channeling his inner artist.
"I found a certificate degree template and I just plugged in Miami University and changed some colors so it was red and white," he said. "I put in, 'Alec Martinez, Bachelor of Science in Accounting.'
"They were completely shocked."
Video: COL@LAK: Martinez beats Varlamov from the point
Ironically, the previous night while walking his dog with his dad, Frank brought up the subject of education again. Alec kept a perfect poker face.
"He was talking to me about what I wanted to do after hockey and asked if I thought I would get my degree once I was done playing," Alec said.
"I was like, 'I don't know.' I just played dumb. Little did he know that I was pretty much done."
Once Alec revealed his secret the next day, his parents were overcome with emotion. Alec recalled his mother had tears in her eyes, but Lynne affirmed, "His dad cried. I didn't cry. I was just so happy."
Regardless, they were both impressed by the lengths their son went to keep the secret. Lynne later found out that most of Alec's teammates knew what was going on.
"Greener knew," she said of now-retired defenseman Matt Greene. "I love Matt. He would take complete joy in putting it over on us. That's how he rolls."
This summer, the Martinezes were visiting Maria in New Jersey. Alec needed a couple of plausible cover stories to explain his mysterious absences.
"One day, he told us he was going to Hoboken," Lynne said. "He was gone for a long time and I texted him and said, 'Are you OK?' He said he was fine. But he was down in the lobby studying!
"He said he had his computer all set up. If we came down in the lobby, he could just shut it down. He did all these really clandestine, covert actions."
After Martinez finally revealed his secret, he had one final hurdle to clear, one remaining test for his financial auditing class. The Kings were on the road to play the San Jose Sharks on Dec. 23, a Saturday.
Martinez studied on the plane and studied some more in the hotel in downtown San Jose on Friday afternoon.
"I just had to sign in and take it online," Martinez said. "It took me about two, two and a half hours. It was a tough test, but I thought I did really well on it.
"After, I went down to the hotel restaurant and ate at the bar. My professor told me he would call me ASAP. My phone rang and he said, 'Congrats, you nailed it. Congrats, you're done with college.'"
Just as in hockey, this also was a team effort.
"I know it sounds like a cliché, but I really couldn't have done it with a lot of the advisers," Martinez said.
Rightfully proud of his latest accomplishment and the joy it has brought his family, Martinez is relieved it's finally over.
"I mean, it was certainly difficult for me," he said. "I'm glad it's behind me.
"And I never have to go to school ever again."