It is very normal. If you think about it, their only experience of life is being in the womb where things are:
Dark
Cramped/tightly bound together
Lying inside a curved, perfectly fitted space
Sounds from outside world are muffled
Constant smell/taste (amniotic fluid)
Warm (think about what it's like in a warm bath)
Constant sound from mum's body - heartbeat, digestion, etc.
Constant movement from mum moving around.
Whereas lying in a cot/generally being in the world is very different.
Cold(er)
Lots of open space, unrestricted (triggers startle reflex)
Flat surface, may be cold
"World" noises are much louder
Unfamiliar smells
Air feels different/strange
Mum's comforting constant sounds are gone
Still
Light
So you can help them feel a bit more settled by recreating some of these things. They also tend to feel most comforted when being held close to you specifically because it ticks several of the boxes (warm, cosy, confined, movement, heartbeat/body sounds, smell of mum).
If you are BF and can feed lying down that's a great one to do. Move covers away, do on a firm flat surface, preferably a mattress, move covers away and one arm between the baby and the pillow means you're safe to doze off or sleep if you want to. This is much safer than accidentally falling asleep feeding in an unsafe situation.
Things which can help them when you don't want to/can't do this:
Swaddling (but only when alone, not when co-sleeping)
White noise / pink noise / any repetitive noise. Baby Sleep app is great for this or you can buy battery powered machines that make white noise.
Movement - being in a swing or hammock. Because these things aren't flat you can't leave them to sleep in them while you sleep yourself, but they're OK for daytime sleeps if you're nearby and supervising.
Surrounding them with a nest type product - again not recommended for unsupervised sleep, when you are asleep that counts as unsupervised.
I tended to find my babies were happier slightly warmer than the SIDS guidance recommends. I didn't feel they were overheated as they weren't sweaty. But one for your own judgement.