Oh yes I agree, don't stress it.
I started at around 4 wks too, but it really is more a case of starting them off on good habits and a long process of gradually encouraging/training them to sleep rather than steadfast sleep training iyswim.
I think the most important thing at this age is to teach your LO that you are always there when she needs you. If she doesn't need you to fall to sleep then pop her down and let her do it herself. If she does need you 10 or 30 mins later, or an hour later or whenever then be there. With that confidence that you are there when needed she will also learn not to need you so much. I spent lots of time doing a kind of AP good habit combo, with singing shushing rocking and putting down when DS's eyes went into the nodding phase. Eventually got him down a bit earlier in the 'seven mile stare' phase. Sometimes rocked the cot a little too or just stood and talked to him in a calming way until he nodded off. Getting the feel of sleeping in the cot is a big thing to learn, no harm in going one step at a time.
Other things you might consider if you haven't already
- introduce a lovie, not to sleep with but to go to sleep with. They can choose their own later on but you can also try to attach them to one. I gave DS a muslin square at every feed time, burp time, cuddle time, sleep time, ok all the time. I never left it with him for sleeping (SIDS risk) but I did lay it next to his face when he was swaddled and I watched him fall to sleep then I'd remove it. When he was old enough to control it himself and beyond the risk age I let him take it for sleeps. He uses it to self sooth all the time. (muslin squares can't be lost and can be laundered).
- introduce a key phrase, this will become a trigger for sleep later.
- use the same song at every sleep. works like a key phrase but lasts longer and can be sung during cuddle time at wind down.
And enjoy your beautiful bundle! x