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Gravity is a property of all matter which suggests that it comes from matter itself.The idea with the big bang is that gravity did not exist originally (meaning that the original singularity was not held together by gravity at any point). If gravity comes from matter, then it would have appeared when matter appeared.
Again I personally agree but this is not a mainstream view. According to GR energy also creates gravity. If this is the case then the universe was born with its full compliment of gravity but without matter it would have been very diffuse. Although energy is supposed to curve space-time, I have not been able to find any experimental evidence to confirm this.