Should I let my baby cry?

Hi parents, I’m a father of a 6 weeks old baby boy. I would like to find out if it is best practice to attend to my baby every time he cries? During the first month, my wife and mother in law were extremely attentive. For instance when my boy wets his diapers and starts crying, they would rush to change it and soothe the baby. On the other hand, I am more calm and would still do the necessary while allowing the baby to cry for a little bit (20-30 seconds more). Being a first time parent, I thought that it’s best that I’m careful with administering the need and am unfazed by the crying. Perhaps because of that my mother-in-law thought that I was inexperienced and hence tended to the baby herself most of the time, which upset me a little. But I acknowledged she had good intentions. After baby’s first month, mother-in-law moved out and went back to her place. It’s now my wife, baby and myself. And boy - I feel like a man and a daddy now! Though there is less help, more inconvenience and less sleep every night, I feel much happier. My boy is on his 6th week now and he still cries. The question I would like to ask is: should I still attend to my child every-time he cries? This is my current protocol: 1. Check if baby is hungry, meal time 2. Check if baby has soiled his diapers 3. Check if baby is feeling uncomfortable (warm, sleeping position) If any of the three is present, administer immediately calmly. If the none of the above is present, 1. Check if there is likelihood of stomach ache, colic If yes, administer some form of massage, carrying the baby around the house, skin to skin touch if no, allow the baby to cry (threshold 10 minutes), and afterwards soothe the baby. If crying still happens after soothing, repeat 10 minutes threshold of crying. I tried doing that over the past two nights and my observation is that my boy sometimes gradually stops crying and goes to sleep on the 8th minute. I noticed that there are two types of crying A) baby has an immediate need B) baby wants skin to skin time, to be comforted and to be carried around by wife and this sometimes prevents her from having proper rest and doing house chores When only situation B happens, that is when I will practise the 10 minutes threshold crying. My objective is to allow the baby to learn to self soothe as well as not to “spoilt” my baby by giving him what he wants immediately. Parents, kindly advise if my approach is appropriate and I would love to hear how I can do this better.