Well, I think it is possible to rank a blog post using just Social Sharing and On Page SEO. BUT, only if the keyword that has low competition.
No off page optimisations mean there are no backlinks. Yes, internal linking helps (which is an on page factor) but gaining that much authority that could beat the competitor and to grab his place, you need backlinks from high authority sites.
So yes, it is possible, when the keyword has low competition but not possible when the keyword has high competition.