In other words, "you" had 100% chance of being you. No luck involved.
It's still useful to think as if different people could have been born in different circumstances. You could think of it as a mental shorthand for the idea that differences between human beings are arbitrary, and it makes no sense to argue that a human inherently deserves an impoverished life over another human.
It also seems a bit homo-centric coming from a human.
BTW, I think we do have genuine subjective probability, even though the universe is deterministic.
This isn't like flipping a coin: it could come up heads or tails.
You must be thinking of some kind of immortal soul.
It may be individually lucky to the person born somewhere (i.e. they had no involvement or choice in where they were born and to whom) but I'm not sure why you would isolate luck to the individual level.
That persons parents made decisions about when, where and how their child would be born. Some parents move countries in search of better opportunities, some were themselves "lucky" to be born where they were. When you zoom out a little it becomes a lot less "lucky" and more of the result of intergenerational decisions and priorities.
I'm not "woe is me" but I was raised in a super conservative family, taught to avoid risk and that a steady paycheck was the ultimate success. It has taken many many years to break out of that mindset and be willing to take calculated risks.
The really hard questions arise when you start talking about what people deserve. Who is to say? We all have a unique frame of reference and experiences that have shaped us.
In the end, the only middle ground we're likely to reach is the mindset of helping people help themselves. To me, the fairness question is more about the opportunity to improve you and yours. Having no opportunities is unfair and must be fixed. The question is always going to be who decides how much is fair?