If my package wasn’t delivered and I choose to pick it up. Can I go to the post office first thing in the morning or do I have to wait for it to be delivered to the post office?

You can leave directions on the notice that you would like to pick it up at the post office at your convience...

The post office only attempts your package 1 time unless otherwise specified. Anytime they leave you a notice, it's best to come in the following day to pickup your item. Lots of times if you come in the same day as when you get the notice, the package is still with the mail man and not back for you to pick it up yet.