Also, I would just like to add that any sleep-training for a newborn (birth - 5 weeks) should NEVER involve cry-it-out. If there is any sleep training for a newborn, it should be very gentle. Extinction and graduated extinction methods are only ever recommended for babies 4 months or older. Before that, it's too harsh, too stressful, and their brains aren't developed to the point where it will actually do any good (and it can do harm).
Make them calm, make them
safe. Then they'll learn.
Our attempts at sleep training resulted in vomiting (kid) and lots of tears (kid and me). We ended up co-sleeping to everyone's betterment so I don't have guidance on that front. However, I did want to mention that there is a wonder week at 9 months so it might not be the best time to start this process because baby's already going through a big developmental leap that is upsetting the status quo.