When you have a small baby, sleep deprivation is par for the course.
Some babies do sleep through the night when they are a couple of months old. DD1 was such a child.
Of course, I put it down to my superior parenting skills and annoyed my friends greatly by giving them unsolicited advice about how to get their children to sleep well too.
Everyone was very pleased when DD2 came along 18 months later, and despite me using all the same techniques as I’d used on DD1, refused to sleep for more than 4 hours until she was 6 months old. I have no memory of when the other two slept through from; I was too tired to notice.