How do we know that? Because that's what the CIA does. It's what it has always done. Regime-change has always been one of the core missions of the CIA. If there is a U.S. regime-change operation, you can bet your bottom dollar that the CIA is at the center of it.
You can also be certain of something else: secrecy. The long-established modus of the CIA is to keep its role in regime-change operations secret, even if it has to lie or commit perjury to maintain that secrecy.
For example, think back to the Chilean coup in the 1970s.
When the Chilean people elected Salvador Allende president, the CIA immediately went into action. It began offering bribes to Chilean congressmen to get them to vote against Allende's confirmation. (Allende had received only a plurality of the votes and, therefore, under the Chilean constitution the Chilean congress determined who was going to be president.)