Many new parents find it a little scary to be alone with the baby for the first time and that is absolutely normal. Follow your maternal instinct and your intuition, and you will see that everything is going well.
Many babies are very alert the first hours after birth. The baby looks around and takes in everything. After that they usually fall asleep for a few hours. They are tired from childbirth and all the first impressions they gained in the first few hours afterwards. As soon as the baby wakes up and is alone, the chances of crying are high. No wonder, considering the baby felt warm and protected for nine months and suddenly that's all gone. The sounds that were so familiar, the heartbeat of the mother and the rumbling of her intestines are no longer there. For the baby, it is nice to be able to sleep in the cot next to the parents, to get used to the new world. For safety reasons, do not let the baby sleep between you.
In general, the new mother sleeps little in the first night. And this is not just because she's busy with the baby - there's the realisation that now it's all very very real, and that being pregnant was the easiest part of the journey.
If you have to go to the toilet at night, you may want to wake up your partner. Occasionally you may suddenly become very dizzy or even faint. Do not lock the door.
Crying babies are often comforted by breastfeeding. Most babies will not feed much on the first day. The baby has sufficient reserves from the womb.
If you are breastfeeding, it is good to feed the baby regularly. This stimulates milk production. Even if you give a bottle of food, you can naturally feed your baby when it cries.
If you have fed the baby and it's still crying, give it your pinky finger to suck and comfort it until it falls asleep.