For practical purposes it is incorrect and should read "At 3 p.m., the test starts" (focusing on the question of what happens at 3 p.m) or "The test starts at 3 p.m." (focusing on the question of when the test starts).
The pattern "At ... starts ..." may sometimes be possible in a poetic or literary style (though probably I would dispense with the comma), but this subject matter seems uns