Try put her in a sleep sack... or swaddle her.
Many infants/babies like sleeping on their tummies... it is more like how they were in the womb as well. But yes, it is not recommended at such a young age.
Is she in a bassinet? Or crib? or what do you mean by "cradle?" Sorry if I"m dense... but my son, slept REAL well, in a Moses Basket. It is WONDERFUL.
Many infants/newborns like a closed in feeling... because it is like the womb, and they like sleeping on top of your chest because they can hear/feel your heart beat and breathing... which is comforting to them. That is how it was in the womb.
Every 3 weeks in an infant is also a growth-spurt time, so keep feeding on demand 24/7... and she may even be needing to "cluster feed" which means a baby feeds even every 1 hour or less. This is also normal and reflects their growing and development needs. Also make sure you are producing enough milk (if nursing) because otherwise a baby will not be full enough.... and cannot sleep and they will always be hungry. Also make sure she is latching on properly... otherwise she won't be getting enough intake either.
For a newborn... they get tired about every 2 hours after being awake. So... gauge it and her....
For night feedings (or anytime).. it should not take 1 hour to get her "so sleepy" again. Usually, if a baby is nursing well and getting enough intake.. they will be real tired/sleepy or even fall asleep at the breast. So, make sure she is getting enough intake. Do you actually see her swallowing and hear her swallowing? Many babies will not sleep if they are still hungry. Many of my friends babies were like that. Their babies simply were not feeding well, nor getting enough intake. Once they corrected that... then their babies slept a TON better and were more regular.
Over-tiredness... yes, it actually makes it much harder for the baby to fall asleep, and to stay asleep, and they actually wake more and have a worse sleep.
all the best,
Susan