It's not always the bigger company that's the prime
I was a sub to Leidos on a contract over at NGA on a big IDIQ, which is a contract vehicle that issues multiple task orders to companies that won a place on the contract.
The IDIQ was re-competed, and on the follow up IDIQ, the task order I was supporting was re-designated to be a small business set-aside, which means only designated small businesses could win it.
The winner by mandate was a small business, but guess who ended up staffing a good percentage of the positions?
Needless to say, they are not a small business.
It's just a goofy thing where a smaller company can sub out work to a much bigger company, which is counter-intuitive.
What's even funnier is that the small business that won the task order was acquired by Mantech, the multi-billion dollar defense contractor.
This is all to say that while it's usually a large company that plays the role of the prime, there are smaller companies that do win awards and you shouldn't neglect them in your search for a 1099 gig. They are sometimes more amenable to subs/1099s since W2s can be riskier for them.