Totally agree. My kids were picked up when they cried, and they have grown up to be confident happy outgoing kids. Its not some kind of a game, babies don't need to be "trained", you should show them some love.
In the OPs case the baby has only been out the womb for a few days. They wont be able to see properly, and when they do open their eyes the light will be quite a shock, likewise with hearing and smell, it is going to be sensory overload for a good while.
If the baby is crying and wants a cuddle, then give it a cuddle, I would say it heartless and cruel not to. You've got something else you would rather be doing?
The idea of leaving a bay to cry itself to sleep is really quite out dated now so I don't know why people still mention it. There is actual scientific evidence to suggest it is harmful to development. Many appearances to child rearing from the past are just not valid with today's understanding. It wasn't that long ago that babies would be given morphine and other drugs to keep them quiet. We wouldn't think of doing that now a days.
One of the evening classes I went to was run by a researcher in this field. Their analogy was like a car with an oil warning light on. The car is not trying to manipulate you, you are not spoiling your car by getting an oil change, it is just a simple sensory feedback. The car is not thinking. babies crying are not thinking, they just have a sensory input that is causing them stress, their crying is their alarm because they don't have the ability to talk.
A babies cognitive ability is far more limited than most people would guess, far less than your house pets. Peek-a-boo is a such a fun game because to a baby when you put your hands over your face you disappear out of existence to them only to spontaneously appear out of thin air later. They have no concept of object persistence.