The baby's body was found in the water by a passer-by at Rough Wood Country Park, off Hunts Lane, in Willenhall, last Thursday, at around 1pm.
Revisiting the scene on Thursday, detective chief inspector Jim Munro appealed for the mother to come forward and for anyone who may have information.
DCI Jim Munro, who is leading the investigation, said: "We are a week on now from when the little boy was discovered here on the canal.
"Today, again, I am appealing directly for mom to come forward, so we can get you the medical support and help that you need. That is our number one priority at this time.
"Also, I am appealing to people who may have information in regards to who mom is, or how the little boy has ended up in the canal.
"I am asking you to come forward, whether that be in confidence, and speak with police, to allow us to understand how the little boy has come to be in the canal.
"But also so we can get mom that support that she desperately needs."
A post-mortem has taken place revealing the baby – who is believed to have been at full-term – died either "during the birthing process or in the hours that immediately followed", said DCI Munro.
But medical experts have not yet been able to establish a cause of death.
Nor has it been established whether the baby was alive when he entered the water, although detectives do not believe that, or how long the baby had been in the water.
The baby's body was found at around 1pm last Thursday by a passer-by who was walking along the canal towpath near to Bentley Wharf Bridge. Tributes have since been placed by the bridge.
In a bid to trace the mother and find more information, officers have visited the area handing out leaflets and carrying out door-to-door enquiries.
Speaking to reporters, DCI Munro said: "Today we have got officers in the area, doing some door-to-door enquiries, taking out some leaflets as well to try and raise the awareness, again, asking people to think back - which is now a potentially two week window - around anything suspicious they have have maybe seen in the surrounding areas."
He continued: "We are continuing to work with experts to establish a full cause of death.
"But at this time we are in the process - a long process - of trying to establish how medical causes have taken place. That may take some time.
"There is no exact cause of death at this time.
"However the information I can give you are the initial findings from the post-mortem, and we will continue to work with experts to try and find those answers.
"Ultimately, it is our belief, at this time, that he was probably not alive when he entered the water. But whilst further tests are ongoing I cannot give you that as a definitive answer.
"At this time, we have got no lines of enquiry in regards to how the baby has come to being in the water.
"Again, that is something we continue to work on, and appeal for people to come forward, who were using the canal towpath in and around the time in which the discovery was made; but [also] in the week leading up to it, to come forward if they may have seen anything suspicious.
"People who have been on the canal towpath, perhaps carrying something, that now in hindsight they believe could have been the little boy.
"Please come forward, and speak with us with, and provide us with that information to allow us to try and understand a bit more of the time frame that surrounds how long that little baby was in the water."
Anyone with information is asked to call West Midlands Police on 101, quoting incident number 1963 of May 20.
Alternatively, contact Crimestoppers anonymously on 0800 555111 or at crimestoppers-uk.org