blockchain – Nothing-Up-My-Sleeve BTC Addresses

I’ve been researching some crypto related concepts and came across “Nothing-Up-My-Sleeve Numbers” and from what I understand I can generated a Bitcoin address that basically comes with an unknown/pre-lost private key, making the address a burn wallet. I’ve come across “ecdsa” but have no idea how it fits into all of this.

How would I go about using a number like Pie to generate a public BTC address with a private key that’s unknown/impossible to guess while also making sure it was generated in a way that’s open and verifiable?

What info is needed to reasonably prove it was generated correctly?

https://en.wikipedia.org/wiki/Nothing-up-my-sleeve_number

I have some minor experience with python but I’d like to be clear on what I’m doing or what opensource tools I’m using.