They can go in from birth, the reasons many people don't put babies in straight away is because a lot of babies like the cosiness of a small space, and in many cases going into the cot means sleeping alone.
We have a single bed in Isobel's room so I sleep in her room while she is in the cot.
The first 3 or 4 weeks we spent all night downstairs as the cluster feeding was so intense and I needed tv to keep my eyes open - me on sofa and her in pram carrycot or on beanbag inbetween half hourly feeds! After that she went into crib in our bedroom while hubby slept in bed next to her. I slept in Isobel's room so I could catch a couple of hours (at that stage every noise woke me up), hubby would get me when she woke for first feed of the night and I would put her into her big cot afterwards and sleep with her for the rest of the night. From 4 months she stopped going in the crib altogether and went into her cot from the start of the night.
In short she's been in her cot for at least some of the night since before a month old. She's almost 6 months and from that point she'll sleep alone.