"As a first time mom with a 5 week old, I love your site and your discussions have helped me enormously so far. At the moment I have two questions on which I'd love your and your readers' thoughts. First, about when are babies able to drift off to sleep on their own? Right now to get the baby down to sleep, I need to rock, jiggle, etc until he is absolutely 100% sound asleep. We do swaddle him, and that helps, but if he is the least bit awake when you put him down, he wakes himself back up and proceeds to screaming within minutes. To be clear, I'm not talking about sleep training, I know he's not old enough, and I'm perfectly happy to nurse and rock until those little eyes close. I would just love to be able to put him down without worrying that the smallest jiggle will mean that I need to start all over again.
Second, about when can babies amuse themselves for a bit of time? For now, the baby seems to need me to constantly entertain him. He will sit in his bouncy chair for a few minutes without my attention, but otherwise if I'm not actively talking, singing, walking, bouncing, swaying or patting, the fussing begins. Again, I know that interactions are incredibly important for development and I'm not expecting independent living. It would simply be so nice to sit next to him on his mat and do something else while he plays.
I'm sure it sounds like I don't want to parent him, and that's not the case at all. I enjoy spending time with him and I've loved getting to know him so far. He's generally a happy little fellow and only fusses when he's trying to tell me something. It would just be good to know if this is his personality and I should get used to it or a developmental thing that will change over time."
It doesn't sound at all like you don't want to parent him. It sounds like you have a 5-week-old and your life has changed in an instant and you're thinking, "What have I gotten into? How much longer am I going to have to be on-duty and present every single minute of the day?"
I can remember being a few weeks in with my first and thinking, "OK, only 17 years, 49 weeks, and 3 days until he's no longer my responsibility." And I loved him so much it made me ache. I just wasn't used to the constant vigilance and demands on my attention.
At this point you're just trying to keep your head above water, really. I think the sleeping has to do with a bunch of factors. The first is personality. Kids just sleep the way they sleep. Some go down best by themselves, some need someone to help them for a long time, some are a mix, and some keep changing so you never feel like you know what's up with their sleep.
Another thing I think plays into sleep at the beginning is their stomachs and their size. There are growth spurts at (approximately) 3 weeks, 6 weeks, 12 weeks, and 6 months. Not surprisingly, these are also times when parents report that their kids started sleeping more easily. It seems like the maturity and additional size that happens at the end of a growth spurt sometimes helps with sleep, too. (Tangentially-related: Did anyone else notice that their kids' pooping schedule changed every time they went through a growth spurt? Or was it just my two?)
But then those combine with the developmental spurts and physical milestones and teething to make it all kind of a two-steps-forward-one-step-back proposition. A grand stew of confusion and tiredness for everyone that sometimes doesn't even make sense in hindsight.
So the short answer is that there's no real age at which babies just start automatically going to sleep by themselves. Your son may need to be comforted to sleep for another week, then hit a growth spurt and start falling asleep by himself. Or he may be one of those kids (like my older son) who needs someone to help him fall asleep (by nursing, or rocking, or sitting in his room) until he's 3 years old, and then suddenly he just starts going to bed easily by himself. He'll probably be somewhere in between.
If you're worrying that your son may need to be comforted to sleep for years, don't despair. Even if that happens, a) you'll survive, and b) it's not all bad. In some respects it was easier to get my older one to sleep because I had a hand in the process. If I did whatever he needed at that stage, he'd fall asleep. My younger son, who is "easier" because he cries for 10 seconds to 10 minutes and then conks out without anyone else, is kind of a wild card. If he has the proper conditions he goes down easily, but if there's anything distracting or he can get free, no one can get him to sleep.
Everyone is going to tell you in the comments section how their kids slept at 5 weeks and then what happened later, so you'll have tons of data points that all add up to "There's no way to tell and you'll worry about it, but you'll also make it through and you'll all be fine."
The playing by himself is a real annoyance, isn't it? You just want to run to the bathroom, but even that's too much. First babies don't realistically give you more than a minute or two until they're able to move or control things on their own (so whenever they achieve some kind of mobility control, whether it's sitting or rolling or scooting or crawling). Second babies get entertained by the first child, so you can get a few more seconds here and there. I think it's totally the age and circumstance, not a personality thing at this age.
One good way to cope with this is to wear the baby in a sling/wrap/Ergo as much as possible, because the baby benefits from the motion and the closeness, and you can get stuff done. You can walk around outside, do some laundry, make a sandwich, etc.
Another thing that I only figured out with my second child is that when you have to leave the baby alone and know he's going to cry, you might as well double up on the unhappiness by turning it into tummy time. Your baby probably cries when he's on his tummy at this point. Since he's going to cry for the 90 seconds it takes you to go to the bathroom or get yourself a glass of water anyway, why not put him on his tummy before you leave? He needs the tummy time, and this way you can at least feel like something productive is coming of your trip to the kitchen.
If you have a My Breast Friend, you can strap it on, sit down at a desk and put the MBF on the desk. Your baby can lie on the MBF and sleep or nurse, and you can type or surf at the computer over him while he sleeps.
This stage is tough on everyone. It's especially tough when everyone tells you to "enjoy this time because it goes so fast" or that "these are the best days" or all those platitudes issued by people who don't have teeny infants. You feel trapped and a little freaked out, and then guilty about not loving every second of it. It's hard to adjust to your old life being gone for a long time, and not really loving the new normal. Even if you love your baby, it's still jarring not to be able to just think your own thoughts for 10 minutes.
But. Things will get easier. You will get some time back. You will get yourself back. You'll have more fun with the baby. You'll hit a good stride together. Be kind to yourself.