Even if his mother had told him that was the case there is a paper trail, for one there is her passport documents, and there are flight manifests and port of entry records that must be maintained for legal reasons.
Her name and possibly his cannot just disappear from such records.
I wouldn't be surprised if that were in fact the case. But in order to obtain pieces of paper reflecting those kinds of data which you can then introduce into evidence, you need to be in a position to do discovery in a lawsuit. Further, that kind of investigation is not cheap to do.
And you recognize that their power to scrub the record books has been very extensive. So it may be that effective access to those documents won't be available.
I do assume further that if my hypothetical time line is correct, the baby would likely have traveled on her passport and there won't be any separate record documentation of his existence. That wouldn't be a particularly difficult issue if you find his mother on BOAC to Vancouver on August 6.
However her passport is likely to have long since vanished. And I doubt that entry records were maintained at Blaine in that period of time. So you would need to find entry records at Vancouver to support your position--they may well exist.