There is an external force. When the child runs inside the crib, the bottom of the crib pushes against their foot; foot and crib are engaged via static friction. In turn, the crib itself is similarly engaged to the floor via friction. So there is a force acting between the floor and the foot, through the crib. This force accelerates the child's body, which can then strike the wall of the crib, transferring some of its momentum to it. In a free-body diagram of the crib and child, this would appear as an external force.
What we have to explain is how an external force acting on the crib move the individual inside it via their foot, given that the crib doesn't move (at that point), and neither does their foot? The answer is that it doesn't. The friction is preventing the backwards movement of the crib when the child begins to fall.
We need to explain walking.
How does your generate an external force when you walk? Walking begins with falling. You lean slightly forward, disrupting your balance, and begin to fall. At the same time, you lift a foot, and extend that leg; the fall accelerates. Eventually, the free foot is planted in order to prevent a complete fall; and the center of gravity vaults over that leg.
In the absence of friction, the resting foot would slide backwards and the body's center of gravity would fall straight down. Because there is friction, the resting foot stays planted, and acts as a pivot; a force is generated between the foot and ground which deflects the center of gravity to fall in the walking direction rather than straight down. In a free-body diagram of the person, this would appear as the external force which generates displaced movement,.
The rest of the walk is just a sequence of controlled falls, with a supply of energy to counteract losses.
Thus, back to the crib. If there were no friction between the crib and floor, (but the usual friction between foot and crib), what would happen when the child starts to move is that the crib would move in the opposite direction. Then when the child bumps agains the crib wall, that movement would stop. There would be net displacement of the crib, but the center of mass of the crib-child system wouldn't go anywhere.