Hi mama! So 1cm at 37 weeks is actually quite normal pa, hindi ibig sabihin kaagad manganak, kasi ang cervix mo pa lang nagsisimula mag-prepare, at bawat mama ang timeline talaga, lalo na first baby mo. Possible within a week or two, but possible din na magsiguro ng dalawang linggo or more, kaya dapat lang na mag-relax ka muna and enjoy the last few weeks habang naghihintay, pero kung may twinges or unusual cramping, best to check in with your OB para sure ka lang na lahat okay.