I was there in February 1970, but more importantly, I worked for the agency. Here is what I know for sure.
While all of the new info is computerized, there are old micro fiche in closed records. They can be located by the family's last name.
NOW, here is what I found incredible. There are huge black ledgers dating back to the 1800's with the names of each child as the entered as well as what happened. Ex. Child's name and date of entry. Parents' name ( not always correct ) and if the child returned home, was indentured out, and sometimes notes concerning a health check up.
Even though the records are hundreds of years old, they are still bound by confidentiality. You would need to write to the agency requesting any info; names, dates, your relationship, etc. They would then need to decide if you are to be given this info. I know records is generally swamped with current workloads so going through the ledgers may not be a priority, and when I was there, people did not even realize the gold mine of info they had in those ledgers.
I would love to have an hour with those ledgers now. In fact, I may just request info from an 1883 to 1910 placement.