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Actually, right about 2 weeks for both of those things. With my 2nd that's when I got my head out of the crazy early days enough to ask those questions of myself and start implementing them. I'd say we started with 50/50 success for drowsy but awake at 2-3 weeks but it just got gradually better. And starting a consistent bedtime routine helped everything feel more sane too.

So I'm trying to figure this out right now too

With DD1, I'm pretty sure we didn't try to put her down without being dead asleep until 5 months. With DD2, I've kind of been forced into it earlier because she wakes up every time I lay her flat in her crib. So it's been working reasonably well since 4 weeks for us this time - she usually sleeps 5-6 hours from that point but I haven't dared try to put her back in the crib after that 5/6am feed because I'm exhausted and she seems more awake. I take her to the living room and nap on the couch while she naps in the rock & play.

She'll be 6 weeks on Saturday, though, so my next goal is slowly trying to put her down earlier each night until she has a proper bedtime. This is hard right now since she wants to nurse nonstop from about 5-11pm... and I know I'll have to learn to put her back in her crib since she'll be waking earlier and earlier.

Good luck!

We did both of those things pretty early!
I did drowsy but awake from the very beginning. Didn't always work (especially during a wonder week leap) but I tried to be consistent so he'd eventually "get" it. I'd say he did get it by 6-8 weeks.
As far as bedtime, I followed the max 3 hours sleeping rule until 6-7pm. If he went down after 6/7 I let him sleep as long as he wanted. Sometimes that was less than 3 hours anyway but sometimes it was more. And I also treated after 7pm as night wakings, not EASY or whatever. So if I put him down at 7 and he woke at 9pm, i kept him in the room lights off, swaddles, didn't talk, no eye contact, etc and feed and put right back down to crib.

I would say an ACTUAL bedtime routine (bath, sound machine, lotion, Jammie's, story, bottle) started by 5 weeks.

I know a lot of people just don't have a true bedtime for newborns but based on my own research and my peds recommendation I felt it was best to establish an early, consistent bedtime and routine right away. Weissbluth, many peds, and sleep specialists all say 5-7pm is ideal bedtime for infants - and that's often why people get a witching hour between those hours - they're actually tired and ready for bed! That was a big eye opener for me.

All that being said, I do believe that the newborn stage is "do whatever works to keep yourself sane", so if doing what you're doing is keeping you sane then go for it. I would seriously start to try both things you asked by 3 months though, since after 3 months is when habits can be formed and harder to break.

We are just about to hit 3 months with DS2 and I'm only about to start trying for a bedtime routine now. He is really difficult to put down as he wakes up either immediately or within 20 mins if not held so it's time he learned how to fall asleep on his own! I do wish I had started earlier but I couldn't figure out the logistics with a toddler to watch as well. Following to see how others did it!

DS1 went to bed late, with us, until 4m ish. Then I did the routine and 7pm bed time.

DS2 started 8pm bed time at 8 weeks. He was a terrible sleeper and it was the only way to get control of the situation.

DS3 is 12 weeks and I've been trying to encourage an earlier bed time for a month. He's just in the last week started going down at 9 instead of 10. Hoping for 8 soon.