No, but plenty of money to be made selling NASA a ride for its probe to Neptune. The private company can build the rocket for 1/10 the cost of NASA, but charge NASA 1/5 what NASA would cost to build it. Boom NASA saves 80% and the private company makes 100% profit margin.
Blue Origin:
https://en.wikipedia.org/wiki/New_Glenn
45,000 kg to LEO announced so far. And unlike Spacex, Blue Origin is very secretive. I suspect they have much bigger things in the works quietly.
SLS is 70,000 kg to LEO in Block 1, which is comparable to the falcon heavy. SLS Block 2 with the 130,000 kg capacity you mention is 12+ years away, and I'd give 5:1 odds it never flies. I'm betting ITS has a better chance of actually getting built than SLS Block 2, and ITS will have 550,000 kg payload to LEO, which is 4x more than SLS Block 2.
https://en.wikipedia.org/wiki/ITS_launch_vehicle