During a two-week trial at Leeds Crown Court, jurors heard that Oscar Abbey's parents found his body after he got his head stuck while trying to crawl through a gap in the bed on November 3 2016.
Craig Williams, the owner of the company which sold the bed to Charlie and Shannon Abbey, had been on trial accused of gross negligence manslaughter.
But the jury was asked to return a verdict of not guilty on this charge on Wednesday, after the defendant, of Park View Road, Kimberworth, Rotherham, South Yorkshire, admitted failing to discharge an employer's general duty under the Health and Safety at Work Act and a count of fraud.
During the trial, the court heard that the Abbeys had bought the bed through PlaytimeBeds Ltd, which was owned by Williams, 37, for Â£655, including delivery.
John Elvidge QC, prosecuting, said the defendant had been the "controlling mind" behind the Sheffield-based firm.
The company made bespoke, MDF beds in a range of shapes, the jury heard.
Speaking about the night of Oscar's death, Mr Elvidge said: "During the course of the night, he wriggled his body through the holes at the front of his cot bed.
"His head was too big to fit through.
"In effect, he choked to death. He was starved of oxygen."
In a statement read to the court, Mr Abbey, 24, described finding his son trapped face-down in the front of the cot.
"I instantly realised he'd gone," he said.
"It looked like he'd tried to crawl out backwards but his head was stuck."
In her statement, Mrs Abbey, 23, said she woke up and "I heard Charlie shouting and screaming 'He's not breathing'.
"I ran to the landing and Charlie was holding Oscar in both arms."
She added that her son had first started using the cot, which featured a slide, on October 28 2016, having been told by Williams that it was suitable for children aged six or seven months.
"At no point was I advised that it was not suitable," she said.
Mr Elvidge said a customer had contacted Playtime Beds in March 2016, complaining that the bed she had bought did not meet standards, but was told by the defendant: "I have been in touch with Trading Standards and they are happy with my products."
The prosecutor said trading standards officers had no record of contact from Williams.
Jurors were told that, even after Oscar's death, the defendant did not stop making beds and did not even alter his designs.
Mr Elvidge said: "Maybe the only reasonable inference to be drawn is that he didn't care at all about the fate of those using his beds."
The prosecutor added that an email was sent to Playtime customers, which said: "There's been a slight issue and the business has had to close for a couple of weeks."
Williams was granted bail until Friday, when he will be sentenced alongside employee Joseph Bruce, 30, of Kimberworth Park Road, Rotherham, who also admitted fraud.
Mr Elvidge said Bruce, who pleaded guilty before the trial started, had been purported to be running a new bed company set up following Oscar's death, but added that this was still Williams' firm.