Yes during early pregnancy your cervix will be firm, hard and will be long and closed until your third trimester of pregnancy.
It is very normal for your cervix to become firm or hard and change position during the early pregnancy.
Your cervical discharge will also change in color and consistency during early pregnancy and during the full pregnancy.
Also during pregnancy your cervix will extend into your vagina and fill with mucus during pregnancy.
The cervix filling with mucus is known as the mucus plug which helps protect the baby during the time in your womb.