A topic that comes up enough that I have a section for it in my personal Traveller documentation. Designed with Mongoose in mind but may be useful to this discussion.
Starting Young
It's one thing if this is part of an overall background that the player wants for their character. It's another thing if the player is just trying to abusing this to "cheat" and get more skills before aging rolls start at age 34.
As a GM, if a player really wanted to start younger and they had a good story for it I'd allow it with some penalties.
Some of these penalties are to reflect difficulties younger characters would have to qualify for careers, survive, and gain promotion. A 12 year old will probably look young. On average, a younger person also wont have the same maturity and amount of life experiences as their piers. The penalties are low enough to still allow for the exceptional character as a child to be equal or more competent than an average 18 year old.
Starting Characteristics
It's best to make a column of youth CMs, or characteristic modifiers.
DEX, STR
For those starting younger, their physical development is not complete yet. I'll impose a penalty but it is recoverable as the character ages back up to 18. –1 CM to DEX and STR for every 2 years they start early (always round up, or is it down since it is a negative?). So a player that has their character start at age 15 would have a -2 youth CM for these characteristics.
Recovery is at the end of a term. If they are over 18, remove all the youth CMs. If they are still under 18, recalculate the CM. So for a 13 year old with a -3 youth CM when they start, they will have a -1 youth CM at age 17 when they start their 2nd term.
END
General health and determination. No change here.
INT
While this is something more innate, I also see it as something that matures to it's full potential as the person matures.
I'll impose a small penalty but it is recovered. -1 to INT for every 4 years they start early (always round up). A player that has their character start at age 15 would have a youth CM of -1.
Like for DEX and STR, recovery is at the end of a term. For the 13 year old with a -2 youth CM to INT when they start, they will have a -1 youth CM to INT at age 17 when they start their 2nd term.
EDU
The characters Education would be reduced to reflect the younger start and lower level of education compared to someone older. -1 for every 2 years they start early (always round up). This is not a youth CM. This is not recovered! You've been busy with a career and not in school. Perhaps you will increase it through character generation such as rolls for EDU on personal development.
SOC: Play it loose. The noble child might start their career early when a family member passes. Same for a young person inheriting the family business. But a noble child who runs away and starts living off the streets committing petty crimes...
Background skills
Background skills would no longer be 3+ EDU DM. A youth modifier of -1 background skill for every 2 years (rounded up) the character starts early will be applied since the character has not had as long to gain these skills.
Careers
At first I thought certain careers should be off limits for starting early, like the military not taking you until you are 18, but if the player gives the character a good story I'll allow it. Maybe the Imperial army won't take a child but some worlds may have groups that force able bodied children to be soldiers. A 16 year old who really wants to leave home and be a scout might pass themself off as their 18yo brother. While a good story is a must, the youth modifiers above still help reflect barriers to entry.