My understanding, based on what I've just read, is that it depends on whether the document was created in order to obtain legal advice.

If you start the document with "Dear Lawyer, here is my story so far including all the incriminating bits" then that is privileged. However if you write "Dear Joe, hide the money from the robbery in rented garage" and subsequently send a copy to your lawyer then it is not privileged. Both of these are true regardless of when you wrote the document or hired the lawyer.

This is always a tricky problem, especially with a computer which may contain both privileged information and unprivileged evidence of a crime. See https://www.justice.gov/sites/default/files/criminal-ccips/l... starting at page 109 for more on how the police are supposed to deal with this.

I think if you start contacting lawyers something like “hey I did a bank heist, I need your advice” before establishing client-lawyer privilege then that communication isn’t automatically privileged by “confidence”.

No you're fine in that situation. That communication is automatically privileged, even if the attorney doesn't take your case, because it was part of a communication soliciting legal advice.

It’s not clear cut if you haven’t discussed terms, representation, etc. the attorney might say, “I’m booked” before asking additional information.

That's irrelevant from the point of view of the privilege applying. What matters is that the communication was for the purposes of soliciting legal advice from an attorney, otherwise the DA could just subpoena an attorney that the defendant talked to but was unable to afford or who was too busy to handle the particulars of the defendant's case.

That's not how I read it:

"The establishment of the attorney-client relationship involves two elements: a person seeks advice or assistance from an attorney; and the attorney appears to give, agrees to give or gives the advice or assistance[1]"

and

"That “special relationship” between an attorney and his/her client is generally established by mutual assent/consent. This is most often confirmed by a written “retainer”[2]"

Other states have similar determinants.

[1]https://www.lsba.org/PracticeAidGuide/PAG1.aspx

[2]https://attorneys.uslegal.com/malpractice/establishing-the-a...