How do I get my first pet Luna to become an adult? Most of my other adolescents have remained adolescent since they grew up, or I captured them.....

It just takes time Luna will grow into an adult in roughly 10 to 26 days or at least that's how long it took my starter pet to become an adult.

Adolescence lasts a total of 18 days, for pets that are Generated or just grew up from Hatchling stage.

For Tested pets, and Generated pets (including starters), you can see the numbers next to the Maturity
As of us typing this, Luna's Maturity section says: "Maturity: Adolescent (479/648)"
The numbers denote the pet's Maturity Hours, slightly different from Age. Age counts how old a pet is from the moment it's obtained (via creation, catching, whaetever), while Maturity Hours denote what life stage a pet is in.
Maturity runs at a rate of 1:1 (maturity hour : hour) with age, but can be sped up by various methods depending on if the pet is Eggling, Hatchling, or Adolescent.

Adolescence starts at 216 (nine days for bred eggs), and the pets reach Adulthood at 648 (27 days for bred eggs.)

Back to Luna specifically, she's (479/648), or about seven-and-a-bit days away from being Adult.

thank you both so much.