Adult fencing fails kids in three directions at once: through it, over it and under it. A kid a few weeks old can push through a stock-fence gap that stops his mother, flatten himself under a gate with a hand's width of clearance, and treat a railed fence as a staircase. So do not simply put kids in the adult field and hope; give them a nursery pen or a reinforced section of field where the fencing has been re-thought at kid height, and keep them there until they are big enough that the main fencing's gaps and rails are genuinely beyond them.
Mesh, gaps and the head-through trap
Line the young goats' area with mesh small enough that a kid cannot push his head through — a head that goes through a fence is not a joke in goats, because horns and ears can make it a one-way trip and a panicking kid can injure himself or be strangled. Check the bottom of every run of fencing for the gap left by uneven ground, and bank earth, boards or mesh along it; kids explore nose-first at ground level. Gates deserve the same suspicion: close the clearance underneath, fit a latch a bouncing shoulder cannot lift, and make sure the gap between gate and post at the hinge side is not kid-width. Walk the line slowly at kid eye level — crouch if you have to — because the escape routes are invisible from standing height.
Climbing, bouncing and launch pads
Jumping out is usually climbing out in disguise. Horizontal rails, diagonal braces, stacked bales, a shelter roof sloping toward the fence, even a water trough near the boundary all become steps in a staircase a kid will find before you do. Move anything climbable away from the fence line inside the pen, prefer mesh or vertical divisions over ladder-like rails, and raise or electrify the top if a determined older kid is clearing it from a standstill bounce — goats can jump astonishingly high from the spot when something interesting is on the other side. A single electric strand at kid nose height inside the pen teaches the whole cohort to respect the boundary early, provided kids meet it in a small space where they can back away and learn, not in a panic.
Habits that keep them in
Fencing is only half the answer; the other half is that kids push boundaries hardest when they are hungry, bored or separated from their mothers and playmates, so a pen with forage, something safe to climb that is not near the fence, and their herd in view produces far fewer escape attempts. When a kid does get out, treat it as intelligence, not naughtiness: find the hole he used before you put him back, because his siblings watched him do it and the gap will be used again within the hour. Build the boundary walk into the day's routine — out with the morning feed, round the nursery pen, eyes at kid height — and set it as a standing duty in KinsLe's Care Teams, assigned and timestamped daily, so the check survives busy days and different helpers rather than depending on whoever happens to remember.