A mediator is a person who helps negotiate a peaceful settlement between two parties who disagree with each other. Here Jesus helps sinners enter into a peaceful relationship with God.
It can be made explicit that this was the testimony that God wants to save all people. AT: "as the proof at the right time that God wants to save all people" (See: [[rc://en/ta/man/translate/figs-explicit]])
"I teach the Gentiles the message of faith and truth." Here, Paul may be using "faith" and truth" to express one idea. AT: "I teach the Gentiles about the true faith" (See: [[rc://en/ta/man/translate/figs-hendiadys]])