Sage Mode obviously wasn't something natural to Hashirama, if it had been then he would have been rampaging or using it in some form when he was a kid, or when he obtained Mokutoun, not only after being a Hokage for some time. Also, it was stated that Sage Mode is something that can only be obtained with hard work and training, even if one has predispositions for it. Senjutsu Transformation might be inheritable, but Sage Mode will never be (not to mention that it would be strange for him to be the only one from his family to obtain 2 special, very different, powers). Hashirama might have been born with some traits that aided him in learning and mastering Sage Mode, but he certainly didn't have Sago Mode when he was born (the same likely goes for So6p's son).
Basing on what we know, Hashirama's Sage Mode most likely comes from the Bone Forest, seeing as that place was mentioned among the 3 legendary places, almost certainly because that's where one can learn Sage Mode and so far we have only seen 3 types of Sage Modes (plus Senjutsu Transformations, but that's different).