Obtaining TS/SCI in Private Sector - Does This Even Happen?

I am taking it by your question that you do not have a TS/SCI.
There are a lot of different paths on this and I am going to vere off topic for a second before I finish.
1) If you are still in the service; AD, NG or Reserves, try to get into a position which would require you to get ANY clearance. Some contracting companies will pay to upgrade your clearance depending on skillset and demand due to the fact that you can at least pass a clearance.
2) If you have a needed skillset that is in high demand, move to an area that is harder to find those skillsets. ie if you are a computer genius move to an area that has positions that require a clearance but has a hard time recruiting IT people.
3) Apply for government positions and be prepared to wait a long time to get your clearance. Our new hires have been taking close to a year. That means working somewhere else while waiting for the clearance process to finish.

Not all government positions go through USAJOBS. Go to different agencies we sites and you will be surprised to find that many post there and not on USAJOBS.

Keep your military TS/SCI Active by talking to contractor recruiters before you get out. Nough said.

Yes for a TS. I had a TS as a government contractor for over 10 years. Never needed to be in an SCI compartment, so didn’t have that. Some contractors may have SCI because of the equipment or data they handle. Having a security clearance as a contractor requires the Government to require it plus your company must be authorized to manage employees with clearances.