The short answer
Not directly. MLS access in North Carolina is limited to licensed agents and brokers who are Canopy MLS subscribers, so a homeowner can't log in and post a listing themselves the way they might on Zillow or Facebook Marketplace.
The flat-fee MLS route
Flat-fee MLS services exist specifically to bridge this gap: you pay a set fee to a participating broker who enters your listing into the MLS on your behalf, while you continue to handle showings, negotiation, and the rest of the sale yourself. It gets your home into the same database that feeds Zillow, Realtor.com, and every buyer's agent's search, without the full-service commission.
What MLS exposure is actually worth
The MLS is where the overwhelming majority of buyer's agents search first. A home that's off-MLS relies entirely on the seller's own marketing reach, whether that's a yard sign, Zillow's owner-listing category, or word of mouth, all of which cast a meaningfully smaller net than MLS syndication does.
Once your listing is live, pricing it correctly matters even more without an agent's market data behind you; see how to price a for-sale-by-owner home correctly for that piece of the process.