In the movie this is a real loose end. It suggests that some other scene (s) ended up on the cutting room floor. The play is by Clifford Odets, not a man to be frivolous or negligent. Recall that the whole business was in the newspaper, it is raised, then nothing happens. Who knows? Also, inconsistent, was the baby it appears, then disappears. One point characters came back from the bar or some place and the baby is nowhere in sight. Altho the kid really was just a device to add to Stanwyck's motivation, and it shows up Robert Ryan's callousness. The dialogue in the film is razor sharp, and movie really under rated.

they mentioned the dead baby under the bridge,
and later a little girl that drowned.
I think this was to put a subconscious idea in our mind that when he left the house with the baby at the end that something bad was going to happen
a little more drama til the end.

Keen observation! Never thought of that. Naturally, I assumed it was something to set the mood, but if you really start to think about, it could mean something, intetntionally or not.
I'm here, Mr. Man, I can not tell no lie and I'll be right here 'till the day I die