[Alan McDougall (OP)]

Science tells us at the moment of the Big Bang gravity was infinite or everything was absolute.

Now it has been proven scientifically that the greater the gravity field, the slower time flows slower relative to that on an object under a lesser gravity field.

Thus my question is how could time flow out of an infinite gravity field of the big bang singularity? Logically it should have kept the universe in a static eternal non-moving moment.

Alan

[IAMREALITY]

I'm not sure why it should've kept it static.  Like you said, in higher gravitation, time slows relative to time passing in a lower gravitation.  Where is your relative here?  With the big bang, it would be relative to what exactly? 

Furthermore, most here I'm sure would be aware that the laws of physics as we know them kinda break down at the moment of the big bang, so I'm not sure if any of it would be relevant in answering the question to begin with.

[IAMREALITY]

I also think you may be confusing infinite gravity at the origination of the big bang with infinite density.  At the very moment of the big bang, gravity hadn't even technically existed yet.  Time, for that matter, likely didn't exist as we know it either and could've been something altogether different.