In 2365, she had recently graduated from Starfleet Academy and was transferred from Starbase 173 to the USS Enterprise-D to serve under Lieutenant Geordi La Forge. It was Gomez's goal to serve on the Enterprise-D for years. La Forge expressed appreciation for her excitement, and mentioned that she could be of better service if she learned to relax a little. Shortly before that, she had accidentally spilled her hot chocolate on Captain Picard. (TNG: "Q Who")
Background information Edit
Gomez was played by actress Lycia Naff. The script for "Q Who" describes Gomez as "a young twenty five to twenty eight year old ensign – who has newly arrived on the Enterprise. She is very energetic, and enthusiastic in an open and ingenuous way, which is both appealing and refreshing." 
In a 2012 interview with Naff, it was noted that her character was initially supposed to be recurring with the intention of becoming a love interest for Geordi, but she was dropped after her second appearance.
According to Naff, "I was supposed to be there for three episodes, because they were trying to find a reason [Geordi] would take his visor off, to justify a reason he would undergo a dangerous surgery to risk his life so he could see again, and the reason was supposed to be because he's in love. They wanted to have us fall in love so deeply that in the next season, he would say, "I have to do this so I can see my beauty." But they also wrote Sonya Gomez as comic relief, as a bumbling ensign with bright eyes who wants to save the world but ends up spilling hot chocolate on Picard, and the feedback they got was that there was no way Geordi would fall in love with someone like me. And I didn't know what they were going for, because we weren't told to play it like it was romantic. I didn't get that clue until later. So we did it more like a little sister/big brother relationship." 
Regarding her proposed third appearance, Naff said, "We also had a major hair crisis. I did two episodes, and I was supposed to come back and do a third, but I wanted to cut my hair. My agent asked if it would be okay, and since I wasn't under contract, they said, "Okay, we're releasing her." So I cut it shaggy, but above the shoulder. I get a call the next week, and they want to redo a hallway scene, and I go back, and they lose their tiny little minds. They were so angry. Everyone was grumbling at me, and making me feel not so great, but LeVar [Burton] was so sweet. He said, "Don't worry. This gives us a chance to do the scene even better." He was so supportive and encouraging, and the scene did come out better. So if you look really closely, you can see the hair extensions." 
In Pocket Books' Star Trek: Starfleet Corps of Engineers series, Gomez appears (in the post-Dominion War era) as the executive officer of the series ship, USS da Vinci, with the rank of commander. Her middle name is given as "Guadalupe". In the Star Trek: Destiny novels, Gomez had been made captain of the da Vinci. In Star Trek Online Gomez became head of the Starfleet Corps of Engineers prior to 2401, and resigned the position that year to be replaced by Miles O'Brien.