Of course it's normal - the average pregnancy is 40 weeks long. Contractions will start when your body is ready to go into labor. When labor starts you'll know it. My labor started at 40 weeks without even any Braxton-Hicks much less any real contractions ahead of time.
Im 39 weeks and i feel nothing is this normal.
I never got contractions until labor was induced with my previous pregnancies. Everyone is different so don't worry.
I am 38 weeks and still not getting them either. Have been 1 cm for a week also.