Question

From the Rabbi’s remarks I understand the following picture: belief in God is a factual claim that relies on reasons. It is admittedly not certain and cannot be tested scientifically, but it is still far more plausible than any other theory, and therefore should be adopted.
The point is that I’ve seen in several places that the Rabbi links belief in God with intuition. I don’t understand the connection between the concept of intuition and the picture described above. Why is it needed, and what does it add? Thanks.