A computer engineer has tracked down the first Apollo guidance computer
I would argue it was  first space flight guidance computer.Technically nazis V1 had analog guidance computer and traveled in space. The same with all later ballistic missiles etc.Early soviet manned space flights (Vostok, Voschod) were fully automated, in case pilot passes out. Americans did not  had that until Apollo.There was even 'password' login :-) [wiki, Vostok 1]> The entire mission would be controlled by either automatic systems or by ground control. This was because medical staff and spacecraft engineers were unsure how a human might react to weightlessness, and therefore it was decided to lock the pilot's manual controls. In an unusual move, a code to unlock the controls was placed in an onboard envelope, for Gagarin's use in case of emergency.[7]:278 Prior to the flight, Kamanin and others told Gagarin the code anyway.