Crying is an inescapable (and stress-inducing) part of babyhood, but I'm solidly in the "just pick up your baby" camp. Newborn tears have a purpose, and there's a biological reason why you feel guilty for not attending to them. You're supposed to pick up your baby. Motherhood is exhausting, though, which is why I think it's helpful to look at this from your little one's perspective. In other words, imagine what your baby is thinking when you pick them up. Sure, us sleep-deprived parents can't know for sure (because science is cool, but not that cool yet), but I have some theories that are worth exploring.
It might surprise you to know that I'm a cry it out mom, but I don't think cry it out and picking up a wailing newborn are mutually exclusive. That's because you don't sleep train a young baby. Contrary to popular belief, I did not ignore the cries of my 8-week-old daughter in need of nourishment, a diaper change, or cuddle time. (My toddler refusing to go "night night," however, is another story.) Rather, I listened to and observed my baby carefully and did everything in my power to make her feel safe, cared for, and loved. Honestly, I can't imagine doing otherwise.
Babies are spectacular and amazing little creatures. They know what they're doing when they ask to be picked up, and I imagine their inner monologue sounds a little like this: