The phrase "convincing proof" means solid evidence or facts that strongly support a claim or belief. It makes something believable or trustworthy. Full definition
So prove to me scientifically that if you can not prove it scientifically it is not convincing proof? (religion.blogs.cnn.com)
They can all be described as the demand for more convincing proof, and strangely enough they come from two quite different directions, both of which were already known in the first century. (religion-online.org)
Admittedly, absolutely convincing proof can not be provided in all instances. (religion-online.org)