The original mythology of the Asgardians DID have tales of Thor and Loki as young adults adventuring all over Asgard. This was before Thor had Mjolnir and he and Loki were still friends (or at least friendly). They used Thor's magic chariot pulled by goats to travel throughout the kingdom of Asgard and its associated lands.
- As to the aging rate of immortal beings, I suspect they have very long childhoods or at least long periods where they get to be relatively free from responsibility until they acquire some wisdom to go with their longevity. This could be as early as 20 but likely last until they reach their early hundreds, at least the span of one human lifetime to be sure.
As to tales of young Norse Gods
I know there were at least a few because one of my favorite tales has to do with an adventure with the frost giants where Thor and Loki were required to engage in contests with the giants.
Being held hostage, the giants agreed to let the Asgardians go free if they could defeat the giants in even one contest against them. There was an eating contest, a drinking contest and a lifting contest.
A young Asgardian or human named Thjalfi (a servant of Thor's because he broke a bone in one of Thor's goats; in some renditions it was Loki) engaged in the eating contest and was soundly defeated. His opponent was so thorough that even though Loki was an incredible eater and appeared poised to win, the giants voted against him because his opponent even consumed the very bones.
Thor engaged in the drinking contest and was soundly defeated as well. He attempted three times to drink from the enchanted horn and yet each vast gulp was shown to barely move the fluid from the lip of the container.
Upset by their turn of fortune (Loki sensed something was amiss but could not figure it out) the giants offered to allow the two of them to leave if Thor would be able to lift their cat from the floor.
He was unable to do so though he strained mightily. He pulled until the very ground quaked and he was able to lift only one paw from the floor before giving up in defeat.
The versions of the story vary widely but the one I remember most clearly had Thor and Loki escaping with the help of an older, wiser giant who revealed the treachery of the giants. Loki would have won the eating contest, except his opponent was not a giant but a magical fire.
Thor would have won the drinking contest but he was drinking from a nearby lake and nearly drained the lake completely (only giant magic kept him from being aware of it). Remember these are supposed to be tales of the awesomeness of the Asgardians and the realm they lived in. Some hyperbole is to be expected.
As you can expect, the cat to was also enchanted. It was magically tied to the Midgard Serpent, Jormangandur which slumbered on the bottom of the ocean in a deep sleep while it surrounded the entire Midgard realm. Thor's efforts raised the creature to the surface and in a rage it caused earthquakes around the Realms.
The older giant realizing if they weren't careful, this contest could get out of hand ushered the Asgardians on their way.
There may any number of potential tales of their childhood adventures (and it makes sense that there would be) since children were often the recipient of such tales and it makes sense that at least some of the time there would be an opportunity to make a story relatable to children or young adults.
I suspect the reason we don't have numerous tales of deities as youths or how fast they age is that these stories are already at least a THOUSAND YEARS OLD. Most were from an era when writing was limited at best and the traditions were primarily ORAL. If there were any such tales, they are likely lost to antiquity; more the pity as far as I am concerned.