"The effect of gravitational field is all persuasive and instantaneous, it does not propagate in the manner that photons do."

A Photon reaches anywhere in the universe in less than a second [it's time].
Gravity would need to defy time- which it might.
But if what you say is true it would make communication at interstellar distances easy. It also would mean computers could compute faster than light- which is a bit strange.

Part of my explanation of Fermi paradox is that communication can't travel faster than light- though perhaps there is some reason communication with gravity has insurmountable technical difficulties. Or aliens as general rule are simply stupider than humans- which I suppose is possible.

"In a hypothetical situation where a photon existed outside a gravitational field and was stationery in relation to the gravitational field, there would be no effect on the photon, but when the photon accelerated and moved into the field, then as soon as it encounters the field it would be affected by the field.

In other words it is the acceleration and speed of the photons (or mass) that determines the time delay of the effect."

Photon don't accelerate [or can be accelerated] as far as I know. A photon can be made to go slower [I.e, through glass]. One can change a photon's vector- and I guess one could call any change of vector as acceleration.

Now, gravitational fields or space-time distortion is not something one could easily escape from in this universe: On Earth we are in it's gravity well, and Earth is in the Sun's gravity well, and the Sun is in the galaxy's gravity well and this galaxy is affected by the gravity of other galaxies.

So, the idea of leaving gravitational fields must be quantified and that quantity can't be zero [because as far as I know, it's not practical to entirely escape from all gravitational fields {if you could somehow do this- you could have some interesting results or consequences}].