yeah, the thing about making a sling from bias cut is you are going to probably waste like half of the material oh yeah there is also some more esoteric weaves that have high elasticity, i never learned exactly how it's done but there is this thing called "sprung" and i think it basically works by forming a grid a bit like that fencing grid thing, i forget what americans call it, but each line of the thread is a zig zag which loops back left and right around the adjacent thread.

Sprang - Wikipedia

yeah, sprang, idk, my mother called it "sprung" anyway, point being that it's a perfect way to make a sling for a baby. it would let you use a strong but soft and quite thick gauge cordage while allowing a lot of stretch. looks like the device you need to make it is fairly simple to build also, probably could be made with broomsticks.