Yes, but it depends on what you mean by "competitive." I've seen pages rank for moderately competitive keywords with little to no backlink building by focusing heavily on content quality, topical authority, internal linking, and matching search intent better than existing results.
That said, for truly competitive keywords in established niches, backlinks still seem to play a major role. You might get some traction without them, but reaching and maintaining top positions is much harder when competing against sites with strong authority and link profiles.
My experience is that great content can get you surprisingly far, but eventually you'll hit a ceiling if the competition has both quality content and strong backlinks.