I saw an Alan Watts video saying some kids had the question something like "If my parents hadn't gotten married, who would I be?" I think that video just got fed to me as a suggestion and I'm not able to find it by a YouTube search. However, an answer that suits adults is good enough. It's too hard to write an answer that children will understand.
If my parents hadn't gotten married, who would I be?
This is a counterfactual scenario. That is, the question assumes as past event a situation that didn't occur. As such, every that would have happened in the counterfactual scenario is unrelated to anything that did happen in actual fact. Instead, we can assume that everything that happened after the marriage of said parents is, broadly, the consequence of the state of the world at that time. We may want to assume that everything that would have happened in the counterfactual scenario would similarly have followed from the same state of the world minus the marriage. Both series of events are thus related to the same state of the world except for the marriage. But the crucial point is that they are still not related to each other. The Eiffel Tower may be said to be broadly the same in both scenarios because it (presumably) already existed before the marriage in question and we may believe that it wouldn't have been affected by the absence of the marriage. However, offspring from the marriage didn't exist prior to the marriage (presumably) and so there is nothing to talk about. We may want to assume that the said parents might have nonetheless produced children with each other for example, but if so, presumably at a different time and the genetic material inherited by the counterfactual offspring would have been very different, and so, even assuming some children despite no marriage, those would not have been the same at all as the actual ones. Further, even if by some miracle the DNA inherited had been the same, life could have been very different, and we are as much the result of our DNA as we are the result our past experience of life. So, the probability that one actual child would have also existed in the counterfactual scenario is rather remote.
The question probably assumes not only no marriage, but no babies to this couple. In this case, any child alive in the actual world wouldn't have existed in the counterfactual world, and so this child would have been nowhere. It wouldn't exist at all... well, except in some worlds counterfactual to the counterfactual world we are considering now, including in our own, actual, world.
I see counterfactuals as essential to intelligence. We take past events, which in reality could not have been otherwise, & we take some useful abstraction, and we imagine 'if..' about the other results.
Then we use that to think about the future. From that comes probability, statistical thermodynamics, many good and useful things. But, they are based on a lie, an illusion: 'if everything was the same, but x result happened instead of y'. Be we can't really, ever do that.
Sensitivity to initial conditions, 'chaos theory', prevents it. But when inputs are narrowed, we can get close enough. Roll the dice. Flip the coin. Enough is the same, to neglect the butterfly on the other side of the world who might have made a tempest.
Your 'What if..' scenario is mirrored in Zen thought, by the koan 'What was your original face?' We are comfortable narrating our life from our earliest memory, as a beginning. Then we wonder about the situation beyond our continuous memory, after death. But, then, what about before..?
Buddhist thought deconstructs the conventional self, long before it considers rebirth. I wrote elsewhere:
Atheists see rebirth in Buddhism, & think it's like reincarnation in Hinduism. But the Buddhist approach is to take the middle path, between eternalism and a soul, and nihilism (or materialism) & everything ends at death. We are never isolated individuals, we blurred into existence, as part of someone elses body, cared for through our vulnerability, and absolutely requiring our community-developed language, to even have the word 'self'. We are built out of the lives of others, and others will take up the masks and costumes that we think we are, until we realise we can put them down. Continuity is a matter of degree, not only with the person who wakes up tomorrow, but each thought, is an expression of a different person than before it. And yet, even after we die, some continuity remains, as our unresolved conflicts and attachments that we use to define ourselves, are taken up by new subjectivities, or points of view.
In Buddhist thought there are other ideas that can help understand this: the 'thousand hands and eyes of Avalokitesvara' the bodhisattva of compassion: by compassionate actions we participate in a mode of being that generalises, beyond our own skin.
Every word of language we use to hone our thoughts, implies the community of practice that shaped them. We've been modern humans for more than 100,000 years, 3,500+ generations. And yet, in our lifetimes more people have been alive than have ever lived. Our programmable, late-to-develop neocortex, lets us shape ourselves to fit society. So how much does our template matter? How much were we ever unique? One set of parents, is much like another.
Imagining ourselves in the situation of others, gives us copying of motion, via mirror neurons; communication via body language & later 'modes of life'; & morality via categorical imperative & Rawl's theory of justice & Indra's Net - the 'compulsive' nature of intersubjectivity: that our intelligence is in our ability to invite others into our view, & be invited by others into theirs.
So my answer: 'First I am you, then you are me'. There are no essences, no soul, to distinguish us. Just events, accidents, or 'There but for fortune go you or I.' So: 'Do unto others as you would be done by', the Golden Rule. Because, not only are we similar, but we depend on each other, implicitly.
Who would you be if your parents never married? You would be me. Or a thousand million beings like us, facing our questions, our struggles, our hopes and sufferings. In Buddhist thought they say, 'Every being has been your mother and father'. Whatever antipathy or grudge, every being has this connection, of intimacy, and deserving gratitude and loyalty, like our parent. And when we correct them, or reprimand them, it should be like that, knowing that, but otherwise we would not be.
The core metaphor that helps illustrate this, is Indra's Net. We exist, in the eyes of others. They exist, in ours. And, we inherit, and propagate this. Causes and conditions.
Like a candle lighting another candle, they are not the same; but, the new light causally depends on the old light: reborn, but not transmigrated. Someone else would have been, so like you, but that there but for fortune go you (or I).
Yet, when this recognition begins to spread, something changes: selfishness shifts to compassion, mutual support. These are marks of awakening, of seeing the true nature of things.
First I am you, then you are me.
The brain technically sees everything through the thinking it does right then. It does its own thinking. It sometimes does abstract thinking. It's theoretically possible for the brain to pretend anything. So it's always going to be as though there's something special and unique about yourself with your abstract thinking. And it's certainly possible for there to be 2 people each of whom does abstract thinking and asserts the sentence "This object is an object of higher rank than any object anyone else will ever conceive of." I kind of feel like seeing everything through the method of thinking you have right then is how you're supposed to do it. Trying to get a feel for what it's really like to have another state of mind is actually a type of focus rather than a wandering mind. However, it is possible to learn in actuality how another person thinks. If you know what sentences just come to them to assert and the origin in their brain of it, then you can accept that as an answer to how they think without feeling it in full. And you're free to do what ever abstract thinking you want including feeling like there is something special and unique about yourself. So I will answer the question of how you could see things through your own abstract thinking and have them make sense with your own abstract thinking.
It could happen that you watch somebody else pick one of 6 objects arranged in a circle without knowing in advance which of them it's going to be. Now if they had picked an object from another of the 3 groups of 2 objects on opposite sides, which one would they have picked? There is no answer. You can similarly pretend that you happened to be yourself and that there is no answer to which person you would have been if everything had gone differently. You could have happened to be a different person even with everything going exactly like it did. According to your abstract thinking, it could have happened that a different number of people existed even because which according to your abstract thinking which person another person is is no real question and only which person you are is a real question.
Suppose you were somebody else. According to your abstract thinking, it could have happened that you had been a different person all along just like it could have happen that your life starting from the recent past had gone differently than it did. Then if you were a different person, what would have happened? That would have been the only life you're ever known and you still would have been wondering what it would have been like to have been a different person and seeing what it's like to be a different person as a nice change rather than being the person you already were. You have the answer you would have been wondering about if you had been a different person. You can decide to be satisfied with it by having some bit of an idea of what it would have been like to be another person and wondering what it would have been like to be another person and seeing that you have the answer.
I've sometimes had one environment that I was sort of learning about and then later had a change to another environment and then learned a different way of thinking. If you've done the same, then you could do abstract thinking taking somebody else's past and pretending you had been that person with their experiences and that you're now experiencing a change trying another way of thinking.