Congratulations on your new arrival!
I started encouraging self soothing at 4 weeks, but my LO would have none of it and really put up a fight. I didn't properly start shush patting until around 2.5 months. You really need to decide what you are comfortable with and it may also depend on your baby's temperament. Some start self soothing easily and quickly, others take a bit more time.
In the early days, I held my LO until she was in deep sleep (cuddled her for 20mins and put her down). She would then sleep for a good length of time and wake to be fed. This was lovely back then and avoided a lot of tears.