Having a small kid also got me wondering how chimps cope with the same problems. I mean they’re 98% similar to us, so the babies must go through very similar stages…
I can only assume since we're all here that the survival benefits of incredibly loud infant cries outweigh(ed) the risk of attracting predators. I'm no biologist, but I can imagine how the fact that babies cry promotes formation of close-knit social groups to help defend against predators in numbers.