Most of the time yes it's normal, also to spot a lil. With my first I didn't know I was pregnant until 8 weeks I thought I was cramping and fixing to get my period. With this pregnancy I found out at 4 weeks lol once I had implantation bleeding I knew instantly.
It's normal to cramp but not severely and not with any sort of discolored discharge or bleeding. Otherwise cramping is usually a good indicator baby is growing!
Some of the cramping is also your uterus that is expanding...feels like.period pains