In general, it is best to put your baby in SNOO awake but drowsy. This helps them learn to self-soothe and fall asleep without being rocked in your arms or at the breast.
However, if your baby is just starting in SNOO and fusses when laid down, calm them fully (swaddle + turn on a strong white noise + feed) and rock them to sleep before gently moving them into SNOO.
Note: It can really help to play a strong white noise in the room as you place your baby into SNOO. That can reduce the chance your baby will notice—and object—to going into SNOO. After 2-6 weeks, they should be ready to put in SNOO drowsy but awake.
Babies naturally outgrow the need for motion by around 5-6 months, and the App’s weaning feature usually makes the transition to the cot quite easy.