Muffin wasn't a climber; she was a little girl. Kacee, my little tomboy, is a climber. Believe me, she was climbing at six weeks of age!
She didn't need any help getting up the five or six-inch step (carpeted) to get onto the flat part to come in the back door. She just climbed up it. She used those little toes and toenails to get her grip and went to town!
So, do be careful. Considering that the first way they get around is wiggling and crawling, it isn't surprising that they climb.