As I recall, distribution is pretty much automatic. Then each judge decides if there should be a conference. I think it takes 4 judges to bring it to conference, but we were never able to move it forward.
I say “we,” because I think that we the people have a right to know whether our supposed President qualifies for his office or not. And he refuses to show us or anyone else any of his paperwork.
Evidently at least one of the “conservative” judges thinks that Americans have no standing to ask whether we have a legitimate president or not.
Every case filed with SCOTUS is automatically distributed for a conference. There usually are dozens-- sometimes hundreds-- of cases listed for each conference. Before the conference, each justice circulates a private list of cases they think are worth talking about. If a case is not on any of those 9 lists, it is not discussed at the conference and is automatically denied. If any justice puts a case on their list, it is talked about at the conference; it then takes 4 votes for the Court to agree to hear the case.