The way to get young/unskilled people to build skills earlier in life is to lower the minimum wage, not increase it.
No one is going to hire a 12 year old for a part time job if the minimum wage is $15. It just increases the minimum skill level to be hireable. But hire them for $7.50 and they might have skills worth $15 by the time they're 18.
I think you overestimate how wage-sensitive most industries are. Most companies today have consolidated enough to have a lot of pricing power - if they raise prices, consumers will just have to buckle up and take it.
We've already had history in the U.S. where the inflation-adjusted minimum wage was way higher than it is today and yet the labor participation rate was also higher than it is today.
But my personal preference is for UBI coupled with a repeal of the minimum wage.
No one is going to hire a 12 year old for a part time job if the minimum wage is $15. It just increases the minimum skill level to be hireable. But hire them for $7.50 and they might have skills worth $15 by the time they're 18.