(I used to work in the cc industry and also for a list compiler.)
Your daughter got on a list created either by a list compiler or from a marketing list sold to the cc company by a credit bureau.
When a cc company purchases a list, they provide a list of demographic data to a list compiler. When they purchase a list from a credit bureau, it’s based on basic demographic and/or credit info (but is NOT a credit check).
Ways that your daughter could have made it onto a list provided by a list compiler: If she has a magazine subscription in her name (like for a kids magazines, like “Highlites” when we were kids), if her demographic info has been ever given to a company that later turns around and sells it to a list compiler (ie - her name and zip code. Credit card offers often target “good” zip codes with high median income or high priced houses, etc.), stuff like that. A lot of kids websites ask kids to enter that info. Then they turn around and sell it.
Your daughter has to have a SSN for IRS purposes, no? If she has an SSN, she may have a “file” at a credit bureau, even though she has no credit history, per se. Maybe she has a college savings account you set up for her in both your names with her SSN attached, something like that. Credit card companies “pre-approve” you based on a list provided by the credit bureaus. When buying the list, they will ask the credit bureau to provide names/addresses of people who “look” like they’d be a good credit risk (btw, that’s why you’re only “pre-approved” and can be turned down once the cc company pulls an actual credit history on you). I bet you dollars to donuts your daughter has a file at one of the credit bureaus and “looks” like a good credit risk because of something linked to her SSN and her zip code and the fact that she’s never declared bankruptcy or had a write-off. Even though she’s a child, a basic scan of her info resulted in her being put on a marketing list and sold to the cc company. Even though your birthdate is a part of your credit file, if the cc company didn’t ask for it, the credit bureau wouldn’t have included it in the parameters it used to compile the list that it then sold to the cc company.
So, in short, your daughter’s name and address is out there in the marketing universe somewhere and got sold to the credit card company.
Sidenote, I often took calls about just this topic when I worked in the industry. My company once offered a credit card to a horse. But that’s because the horse’s owner named a financial venture after his horse, therefore his horse’s name and “address” was out in the world, available to be “picked” and compiled onto a list.