Nobody has any proof, but it's strongly suspected. The NSA wrote or had a hand in writing every widely-supported encryption algorithm, and they have a military-scale budget (seriously; the NSA's non-clandestine budget is larger than the entire military budget of every country except the US and China) to spend on hardware to brute-force encryption. Cyberwarfare is a top strategic priority of the US Military, and cyberwarfare is made much easier when you can break encryption.
They have the motive, the resources, and the knowledge to break encryption routinely. It's also standard tradecraft for a spy agency to hide any proof that they have a capability to create uncertainty among their enemies whether or not they do. So no, nobody has proof that the NSA can break encryption, but we do have proof that they have everything they would need to develop that capability.