I am not a fan of any particular methods for teaching babies or children to sleep. I prefer that parents understand how learning works and make decisions based on that. For example, the behaviors we give attention to will happen more. If you pick your child up when they cry, they will cry more often - that is simply how learning works. I am therefore not a fan of methods that teach parents to go to the baby every few minutes as I believe that to be a slow form of torture, as you never actually give the child a chance to learn to fall asleep, but rather make it more challenging by reinforcing their crying at varying intervals, like a slot machine.
What I recommend
I prefer parents choose one of the following options:
Either co-sleep, with all that comes along with that, taking full responsibility for it. That means making the bed suitable for both parent and child, night feeding (hopefully with both mother and baby staying mostly asleep), and possibly co-sleeping during the day as well.
Or, actually give the child a chance to learn to fall asleep by putting them in a separate sleeping space, drowsy but awake, and then leaving them to sort it out while a parent monitors for safety by listening from a distance for any significant changes in crying.
How to teach independent sleep
If parents are choosing to teach their child to fall asleep independently, they should try to do this from the earliest age possible, typically 3-4 months, because the longer they wait, the harder it will be for the child who has had more learning experience with being put to sleep by a parent. Parents can also practice healthier sleep habits from birth, such as lots of attention and feeding during the day and encouraging the typical one longer stretch to happen at night.
Will this psychologically damage my child
Of course not attending to crying children is stressful for them. So is encouraging MORE crying by not teaching them to fall asleep from a younger age and continuing to put them in a separate sleeping space. The research on cortisol levels in the morning of both mothers and babies who have not implemented any of this and continue to try and put their babies to sleep in a separate sleeping space while picking them up throughout the night in response to crying is more frightening.
Ultimately we want our children to have the capacity for self-soothing in addition to knowing they can access it from their parents.