Assume every goat is testing every fence every day, because it is.
There is an old line that if a fence will not hold water it will not hold a goat. It is an exaggeration, but not by as much as you would like.
Most fencing advice assumes cattle or sheep. Nigerian Dwarfs are neither. They are small, flexible and persistent, and they go under and through rather than over. A plain wire fence that holds a cow is an open gate to a miniature goat. A standard ringlock built for sheep has apertures a kid walks through without breaking stride.
Kids are the real test. A four-week-old kid will find a gap you would swear was not there, get through it, then stand on the wrong side screaming for its mother while you rebuild your assumptions. Adults test differently — they lean, rub, stand on things and work at latches until something gives.
Almost every escape comes back to a gate. The gap underneath a farm gate is goat-sized, the gap at the hinge end is kid-sized, and the latch is a puzzle that a bored goat has all day to solve.
Fix it by filling the gap under the gate with mesh, closing the hinge gap, and using a latch that needs two actions or a different grip to a nose — a chain and snap clip, or a slide bolt with a clip through it. Spring-loaded latches that a goat can nudge upward are not latches.
Make it a habit to close gates behind you even when you are coming straight back. Goats notice.
The things that catch people out, over and over:
A pallet, a stump, a woodpile, a water trough, a stack of star pickets or a parked trailer beside a fence is a launch pad. So is a tree with a low fork. Walk your fence line looking at it from a goat's point of view and move anything within a body length of the wire.
The same goes inside the paddock: goats need something to climb, and they will use whatever you provide. Put the climbing frame in the middle, not against the boundary.
Fix your fencing before the goats come home. The first escape teaches them that escaping is possible, and that lesson is very hard to un-teach. A goat that has never got out mostly does not try. A goat that got out once will spend the rest of its life auditing your fence.
The practical order: fence the small paddock or yard they will live in first, get them home into that, and then extend. A secure small area beats a leaky large one every time, and goats need far less space than people assume — it is almost never acreage that limits you.
When you think you are finished, walk the whole boundary slowly and look at the bottom 300 millimetres. That strip is where you will lose them, and it is the strip nobody inspects.