The age at which babies should be able to fall asleep on their own is between 4 and 5 months of age.
It's all different for all babies but by 5 months at least the baby should be able to fall asleep on their own and if your baby is crying it's okay to let them cry it out until they fall asleep.
Just make sure the baby has been fed, has a clean diaper etc and if all that is done and the baby is okay then the baby can be let alone to cry itself to sleep.
During the first 6 months of the babies life you're likely not gonna get much sleep yourself because some babies do wake up at night crying and if they do wake up crying make sure they are okay and see if they need a middle of the night feeding and if so feed them a bottle of formula.
Also check their diaper and make sure it's clean as well.
If so then you can let them go back to sleep.