I had a similar issue in my family. The first child was a daughter
who died at childbirth. One story was that she froze to death while my
grandmother was being cared for, but that sounded unlikely. My one
advantage was that I knew if she existed she was born in Manhattan.
After talking to many family members without any result, she was
finally found on cemetery records as buried in Staten Island as baby
SLATAS, no given name. The death certificate listed her as stillborn.
My point is, there are many possible ways to search for this child. I
would start in the area where the family first settled and look for a
death certificate or cemetery listing that might fit.
Searching: SLATAS, SLONIMSKY and more