I started when my lo was 6 wo, but it was very difficult. He cried a lot, and that's when he was diagnosed with reflux, so I stopped sleep training and let him sleep on my chest until he was 4 mo. That's when I started sleep training seriously. My lo reacted great to sleep training, so it took me around 1 week of constant shpat at all naps. Before he was 4 mo, I tried shpat, and if it didn't work, I rocked him to sleep, but I tried not to stress too much about it.
So, try shpat and give it 20 min, but if it doesn't work, then do whatever is necessary to put your ds to sleep. (for example, the swing). Your lo is too young, so it is normal that he needs you more for falling asleep. He doesn't know how to self-soothe, so that's why he needs you. Remember babies sort out day time sleep from 3-6 mo, and nighttimesleep from 0-3 mo!
So, enjoy your newborn, and try not to stress too much about it, you will have lots of time for sleep training!