It depends, do you know if the child was adopted formally or not?
In those days children were adopted informally often for life, by family members, or good family friends, or even by 'arrangements'to strangers via a church connection, if the mother, or grandparents (if mother/father deceased) couldn't cope or afford to keep a child.
Sometimes in an 'informal' adoption, the adoptive parents also used to change the forename of the child, and in some cases the surname also,if different from theirs, if they were passing off the child as naturally their own, if they had moved to another place.
Also, if a child was born illegitimately to an unmarried daughter, the parents would send the daughter away to a relative living in a different town/city/country, to hide the birth from neighbours and relatives in their own town/city before the pregnancy showed. The child would then be adopted away, either informally or formally before the daughter came back home.
In some cases, mothers of pregnant daughters then took on the child as their own, feigning a pregnancy of their own to cover the birth, especially when children were produced every 18 months.
I've found 3 adopted away children in my family, the latest was in 2023, an 80 year old man living in Edinburgh. DNA links in Ancestry helped but is not always necessary. One of my successes wasn't DNA linked to me.