Was it ever common around the 1930s for families that had adopted a baby to announce their child's arrival as if it was an ordinary birth?

I am researching an unexpected match in a number of cousins' DNA results. The ethnicity analysis suggests that this person likely has one, but not two, Jewish biological parents, and the strength and pattern of their matches suggests extremely strongly that this person is indeed a biological relative of our family. They were born in 1936 and appear to have been raised in the US state of Georgia by parents who were likely both Baptists. (Much of my family also lived in Georgia in 1936, although mostly not in the part of the state where this person was raised.)

Until I succeed at contacting this person's family, I am trying to gather as much information as I can on my own. One of the things I'm trying to figure out is whether I can narrow down the candidates for the person's possible parent in our family by determining whether that parent is likelier to be male or female. So I'm looking at two main possibilities: an extramarital affair involving the person's mother (suggesting the link is a male cousin in my family) or a baby being given up for adoption (suggesting that the link to my family might well be a female cousin). If I can be pretty confident that this isn't an adoption situation, I can zero in on one of the male cousins as the probable link.

The curious thing is that today I came across a couple of newspaper items that likely involve this person's family. One is apparently of a baby shower for the person's mother, given by their Baptist church. The other, about five weeks later, announced their birth.

So what I'm wondering is: was it a thing back then, especially in the US South, to have showers and birth announcements for adoptive parents? Or does the mere fact that these happened suggest that it's unlikely that a new addition to the family was adopted?

There's a second, particularly fascinating wrinkle involving this genetic genealogy mystery, but I'll save it for a follow-up.