The infant, who was discovered by a dog walker in bushes at a park in Kings Norton two weeks ago, has now been discharged from hospital and said to be 'doing well'.
Named George as he was found the day before St George's Day, the baby was found by a dog walker on an area of open land known as The Mound off Shannon Road, Kings Norton, at 5.30pm, on April 22.
West Midlands Police confirmed George has now left hospital with foster carers, with the force still yet to track down his mother.
Detectives have been been appealing for help tracking her down since George was found but to no avail.
In a direct appeal to the mother, Detective Inspector Neil Hunt said: “To you, mom, I don’t know why you left baby George here but giving birth is a significant event and I am concerned you may need medical treatment and support.
“You’re not in trouble."
Police had also released CCTV footage showing a woman walking along Shannon Road just before 5.10pm on the day George was found, saying they believe she may "have vital information about what happened".
Baby George was thought to be just a few hours old when he was found, weighting 7lb 4oz.
He was discovered wearing grey leggings and an orange and white striped t-shirt, and wrapped in a blanket on a quiet hilltop clearing, partially surrounded by vegetation.
Detectives have been handing out leaflets in the area George was found in a bid to encourage witnesses or anyone with information to come forward.
Anyone with information has been asked to get in touch with West Midlands Police either by Live Chat or calling 101, quoting log 3476 of April 22.
Information can also be given anonymously, via Crimestoppers, on 0800 555 111.