Many credit card issuers have age restrictions for listing authorized users, but many do not. If you have a 1-year-old child, you can list them on a non-age restricted card as an authorized user to start building their credit from a young age. The AU (authorized user) doesn't need to do anything at all, just be listed as an AU for a card which the holder maintains in good standing.
Some explanation about credit:
The way the US credit system operates is not at all in favor of the user. Everyone starts with a 0 credit score (as opposed to many European models where everyone begins with a perfect score and it is up to the individual to maintain it), and that score only goes up when the user is put in charge of handling a line of credit, which could be a credit card, an auto loan, mortgage, or personal loan. The way they handle this line of credit and other additional lines of credit is what drives their credit score up.
One of the factors of calculating credit score is the age of accounts, which is the average age of all total lines of available credit. Meaning: if you have 2 cards, one from 10 years ago and one you just got today, your account age is 5 years, not 10. And if you close that 10-year-old card after getting the brand new one, your account age drops even further to 0 years.
Account age is 15% of your credit score. There are only two factors that have a higher impact: Revolving Utilization (30%) and On-Time Payments (35%). On-time payments is self-explanatory (pay your balance, IN FULL and ON TIME, every time). Utilization is the percentage of credit you use across all available lines of credit. Going back to the 2-card example: if your first card has a $6,000 limit and your second has a $4,000 limit, and you spend $100 on credit for that month, you have a revolving utilization of 1% ($100 is 1% of the total amount of available credit, which is $10,000). Whether that $100. is spent all on one card or split in any amount between the two cards is immaterial; only the total amount matters. Also, 1% is ideal for building credit, because it shows lenders that you are capable of managing large amounts of credit. Anything over 10% sends a different message.
How being an AU works:
When you add an authorized user to a card, that person's credit score will go up because that person has essentially been granted a line of credit to maintain. But they don't have to do anything at all to maintain it. That still falls on the card holder (in this case, the parent). The parent still has to pay the bill IN FULL and ON TIME, every time. The AU need not be issued their own card, nor do they have to make any purchases whatsoever.
The concept of the authorized user was designed in part to help young people build credit without needing to get their own card, which is often not always feasible with a scored score of 0. This is why some card issuers have no age restrictions on their cards – to allow young people, even toddlers, build their credit so they can enter adulthood with 10 years of credit history, 15 years, or more.
The catch is that this credit history is attached to the card on which they are listed as an authorized user, meaning: the card holder cannot close the card (closing credit cards, even those not in use, is generally never advisable), and must maintain that card in good standing by paying their balance IN FULL and ON TIME, every time.
Putting your child on a card as an AU is not meant to give them a perfect score when they turn 18 or anything of the sort, but to help give them some credit history when they are looking to apply for their own cards, take out an auto loan, or anything else in which an interest rate is determined in part by the person's credit score.
Here is a link to more information, including a chart of which card issuers have age restrictions and which do not.