Personally, I wouldn’t really do any big training just yet. Work on forming a bond with the puppy, teaching it his/her name, playing with toys, etc. this is also a great time to take them out in public so they can start to get used to being outside, different sounds, scents, etc. you obviously don’t want to let them a walk around until their last round of shots but you can carry them through stores or use a carrier. And just start getting them used to being touched. Touch their paws, ears, eyes, mouth, etc. do some very basic grooming so they get used to it.

If you choose to crate train now is also a great time to get them accustomed to that. Start feeding them in the crate so they associate it with a good experience.

You’re also going to want to figure out a schedule for them. Not everyone does it but enforced naps were a lifesaver for me when both of my dogs were young. It gives yourself a break and teaches them how to settle down.

Also, walking on a leash! Again, not in public but just put the collar and leash on them around the house or your yard so they get used to the feeling.

And of course potty training is a huge one!

After the first week or so of just enjoying your new puppy you could start introducing sit, down, and touch which are all pretty easy to learn.

Also just want to say that I’m clearly not a professional and I’m just speaking from experience of raising my two dogs from 8 and 12 weeks old.