In my case, the conversations took place after Snowbunny and I fell in love. I'm sure that makes it harder, the ideal is if you can label yourself as polyamorous before you have any partners. Unfortunately, we live in a very mono-centric world, and most people haven't even heard of, much less considered, polyamory.
Just so you know, the term metamour refers to another partner of your partner.
Say there are three people, Apple, Berry and Orange. If Berry is dating both Apple and Orange, those two are each other's metamours.
As for your question, it depends on whether a polyamorous person is solo or coupled, I guess, and if you meet a potential dating partner organically in person, or if you meet on a dating site, a discord, in an online game, etc.
Generally it's a good idea to let someone new you are dating as soon as possible that you don't date exclusively, but are practicing ethical non-monogamy, so people don't get the wrong idea.
But if you are talking about a formerly mono couple in which, after being together for a while, one or the other member decides they want to "open up," that's different.
In my case, my partner and I warmed up to the idea of poly before either of us was seriously interested in anyone else. The actual "let's go poly" talk happened when he had a crush on someone else, but since we already talked about poly on an abstract level and both liked the idea, it was an easy transition. Are most mono-to-poly transitions like this? I doubt it.
I definitely think it's different for anyone. Our world is still very "mono-centric" as Kevin said, so it's probably going to be awhile before these conversations are prior to new relationships with people. I "came out" out to my husband as poly after we'd been together at least five years, when I learned it wasn't a choice but just who I am. It took about a year before he was okay with it and, after several years now where he's learned our relationship is not diminished in any way and actually stronger in others, it's a really positive part of our lifestyle.
Your first post is short, but I get the idea that you are talking about a married or long-term couple, where one or both decide they want to open a closed mono relationship to polyamory.
What is the reality?
Has one of them become deeply attracted to a third party?
Does one of them have needs that have been requested but those needs can not or will not be met by their mono partner?
Is it just a philosophy of love one or both members of the couple find exciting and worth pursuing?
Did they read articles, see TV shows or videos, meet and talk to some happy polyamorous people?
Are they confusing polyamory with threesome sex or some other kink, perhaps?
If you're asking about when to open up a monogamous relationship, definitely have that conversation BEFORE meeting a new person you'd like to date.
"Would you ever consider an open relationship?" is a better start to a conversation than, "Can we have an open relationship so I can date X?"
Some couples do open up in that context (one person having already met and developed feelings for someone else), but it's very challenging and painful for the blindsided, monogamous partner.
The title question is when does this conversation typically occur? What we see here is either a love connection made that spark ignite that drives the push to change the dynamic, or there’s a situation of needs not being met and a desire to expand options. And yes, timing will effect the outcome. Having someone selected and waiting in the wings will make the process harder, IMO. All the philosophical arguments fall flat.
For me, when I entered into my relationship with my now wife around 2000, we went into it being "open". Poly happened by accident with one of our threesome partners, when I fell in love. There wasn't any communication just a swift kick to the nuts and then lots and lots and lots of work on accepting I can love more than one person.
My wife found it infinitely easier, freaking hippy haha