when I read that Gagarin was not the first man in space ... and some suggest that both Us and soviets lied ... so I'm entitled to be suspicious.

Apples and oranges. The Soviet space program was undertaken in secrecy. Missions were not announced until successfully completed. This makes it possible for the Soviets to lie like that. However, the U.S. space program was undertaken in full view of the public. The public saw NASA's successes and failures. The fact that the Soviets were apparently able to perpetrate such a deception does not prove it was possible for the Americans to do the same thing.