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Anyone can at any time; just statistically unlikely for most young people.

I said you have to be lucky

Read carefully :)

Child mortality rates were over 40% in 1800, so yeah, even a child had to be lucky to get cancer in the past.

I suspect the numbers were quite high far more recently than that. From a Reddit post, noting the inflection point occurs at 1900 rather than 1800:

<https://www.reddit.com/r/rootsofprogress/comments/esgqsv/inf...>

Chart is sourced from:

<https://www.jstor.org/stable/2173395?seq=1>

The other thought that I've had is that we're exerting far less selective pressure on huamn infants now than a century or so ago, at least in modernised countries. By which I mean both rich and middle-income countries, as well as quite a few poorer ones which do have basic sanitation, hygiene, and healthcare availability. It's the first increment which matters far more than the last.