“Noah did so; just as God commanded him, so he did.” (Bereshit, 6:22)
“Noah, with his sons, his wife, and his sons’ wives, went into the ark because of the waters of the Flood.” (Bereshit, 7:7)
Rashi suggests that even Noah’s belief was limited. He believed and he didn’t believe that the Flood would come. Therefore, he didn’t enter the Ark until the waters forced him to do so.