Henry/Page baby 1935/36 CO or NM

We have been told several different stories, so it is difficult to know how much to disclose, because one small error could result in someone thinking that they are not the right child. But I will post as much as I think I can without total chaos. My mother and I are looking for a baby my grandmother put up for adoption when she was in her early twenties. When my grandmother talked to me, she said the baby was a boy. She also told my uncle the baby was a boy, however, she told my mom that it was a girl. Currently we are searching for a boy, but can't be certain. My grandmother told me that she traveled to Denver, Colorado to have the baby and put it up for adoption. My great uncle was under the impression, however, that the baby was put up for adoption in Las Vegas, New Mexico. Currently we are searching the Denver area. The big mystery is what exactly happened to the baby. I was told he was put up for adoption. My mom was told that the baby was stillborn. We do not have an exact date for the birth. It would most likely be between the November 1935 and October 1936, but could extend to the end of 1936. At the time, my grandmother would have been 22 years old. Her maiden name was Henry. The father's last name was Page. They were married for a brief time, but we do not know if my grandmother was using his name at the time the baby was born. This is all such a mess for us to try to straighten out. My grandmother was ill the last 4 years of her life and couldn't remember specifics about what happened. The father died in 1945, and never told any of his new family. We have letters that he had written to her, but they are very vague and only imply the existence of a pregnancy/birth/adoption. We are unsure how to move forward with our search, but appreciate any help anyone may have to offer. Thank you, B & M