28 weeks gave birth to my son. It’s been three months since then. He usually sleeps well, but on a few occasions, I noted that he appeared disturbed while sleeping but did not wake up as if he were experiencing a nightmare. When I Googled it, I found varying responses, with some stating it’s not possible till they’re older and others saying yes.
Indeed, REM sleep, which is linked to dreaming, occurs in newborns. They presumably dream of horrible things too. Though I’m not sure what the topic would be. Mom poops and doesn’t look me in the eye? Boobs came off?
My infant experiences nightmares. It is obvious that whomever says something is impossible has no idea what they are talking about. In his sleep, he cries and screams nonstop. It’s quite depressing 
Fortunately, it doesn’t stay long and doesn’t happen too frequently, but he has been doing it since he was five months old, which may have started as early as one month. I simply pick him up, hold him, and murmur that I love him and everything will be well. Soother also provides assistance.
When my little one cries while sleeping, I joke with my wife that she’s seen dragons in her nightmares 
Maybe he’s seeing dragons lol 
It isn’t conceivable in theory because their minds are like blank slates.
Sometimes when my LO cries in her sleep, I’m not sure if it’s because of trapped gas, a desire to poop, or a dream that I’m taking the titty away permanently. Since she is just nine weeks old, her digestive issues are most likely to blame, yet she makes the same expression when she falls asleep after eating and wakes up without nip. Absolute destruction.
At seven weeks old, my daughter is probably experiencing infant nightmares. She cries out in sleep, or at least her expression tells me so. Her noises and gassy/poopy face are so unusual, hehe.
My son was born at 35 weeks and is now approximately 10 weeks old. Over the past few days, we have noticed that, based on his facial expressions and noises, he appears to be dreaming rather than having nightmares. However, it’s only guesswork because there’s no practical method to test it.