Yes a baby should be picked up every time they cry and you should soothe them and check on them and hold them until they are at least a year old.
Babies will usually cry a lot especially at night during the first 6 months and you should pick them up every time because the baby is wanting you for comfort or feeding, diaper changing etc.
Babies cry as a way of telling you things because they cannot talk yet so always pick your baby up and hold them as much as you can.
The crying will eventually stop and you'll actually miss it.
A baby can usually soothe themselves to sleep after they reach 3 months of age and beyond.
Before the baby reaches 3 months of age you may need to help soothe the baby to sleep but after 3 months of age the baby should be able to get themselves to sleep without you needing to soothe them.
Sometimes babies will need to be rocked in your arms to help them sleep as they love the rocking motion.
Then you can place them in their crib or bassinet after they fall asleep.
Some babies will still need the parents or caregiver to soothe them to sleep until 6 months of age as it's all up to the baby.
All babies are different and have different requirements but by 6 months of age most babies are able to fully soothe themselves to sleep.
A pacifier can help some fussy babies fall asleep and soothe them as well.