#1, most people who take care of their bodies will live long and healthy lives. So the first tool is just to take care of yourself through diet and exercise and watch your risk of deadly diseases plummet.
#2, insurance exists and the medical field is extraordinarily effective. Rich people beat all kinds of conditions. Worried your insurance isn't good enough? Buy more. Keep making more money, and keep buying more insurance. Insurance is tool #2.
This may sound harsh but I really don't know a lot of people, in America or elsewhere, who take care of their body, have a Cadillac fantastic insurance plan, and are worried about illness destroying their life. People who are already unhealthy, on the other hand, or don't have great insurance, are worried about this constantly. Now it's unfortunate that society can't guarantee that optimistic state of mind and health for everyone but until it can, it's diet, exercise, and more income that you funnel into more insurance, for you and your family that are the solutions.
After a diagnosis these tools, especially #2, start becoming less effective because now you've got a pre-existing condition and in particular you're kind of stuck with whatever insurance you had when it happened. So the urgent message here is to get on this stuff now, and sleep better tomorrow (and live longer) because you did it.
To your point though enough insurance and regular visits (and screening — does insurance always pay for that?), you might dodge a bullet that your ancestors caught.