How soon can I sleep train?

I’m desperate here. My eleven week old is getting harder and harder to put down and then doesn’t stay down for long. I know the general advice is four months for sleep training. Our pediatrician said six months (!!). We actually sleep trained our first at three months with great results, but now I’m worried we damaged him unknowingly (though he is a great independent sleeper to this day at three years old). I’m just so tired and frustrated and want to sleep!

We don’t really have a schedule yet, but I follow eat play sleep and try my best to stick to appropriate wake windows, though he fights naps during the day as well so I get the sense he is sometimes overtired.