If an event occurs at a point in space time what will an observer experience first, it's gravity or the light from it? Let's assume a person is close enough to an object in space time to be able to observe it's gravitational effects and the light coming from it.
If that object suddenly pops out of existence (hypothetical situation), what will the person observe first,


The gravitational field's absence
The object disappearing (light stops coming)


P.S.- pardon me for the noobness of this question, physics isn't one of my strongest subjects.
it's an interesting question. It could ask about any violent transient effect that produces light and gravitational waves, though "popping out of existence" is the ultimate step function. 

electromagnetic (EM) radiation is slowed very slightly by the presence of interstellar medium (especially by free electrons) and it's wavelength dependent. The image below from this answer shows the lower frequency radio waves arriving later than the higher frequency ones due to such an effect.

The farther away an object is, the larger the time difference, so this technique can be used to determine a likely distance for a given object.

So if you relax the term "light" to include a wide range of wavelengths which many astronomers now do, you can see a quite a big delay.

Answers to How fast can and do gravitational waves travel? say that gravitational waves generally travel at the speed of light, and answers to Have more recent LIGO/VIRGO gravitational wave measurements narrowed down the speed of gravity further? addresses experimental confirmation. I've never heard of an "index of refraction" for gravity that deviates from unity and could slow it with respect to the speed that an EM wave would travel between the same two points, so I think it's probably safe to assume that it will always come before the EM waves.