There are no guarantees for injuries. Everything is probability, and it's about balancing the probability of getting hurt with the probability of getting better. Increasing mileage is one of the most reliable ways to get better (very high probability of improvement with a mileage increase). There is usually a limit to mileage for each event where the gains start to get very small (in my experience around 80-90 mpw for the 800, 100-110 for the 1500, 120-130 for the 5k, 140-150 for the 10k, and 160-170 for the marathon), but up until that point a mileage increase will often result in better times. Now, the probability of getting hurt looks kind of like the inverse. At low-medium mileage, the probability of getting hurt is very low, and it doesn't increase much for a little while. However, right around 50-60 mpw, it begins to increase more significantly. Every mile past there it is increasing exponentially, and by the time you get to 140, the difference between that and 150 is actually extremely significant. The ideal place to be is probably 10-20 mpw below those ranges, where you are getting close to the same amount of gains but with a lower risk of injury. It's important to remember that different athletes can handle different things; those are not hard and fast rules.
However, there are mitigating factors. Good diet and sleep is one of the best things you can do to prevent injuries. Strength training, especially in the hips, core, and lower legs is also very important. Proper stretching and rolling (very important that this stuff is done correctly or it can make the issue worse) can also be of help for some. Just being young helps; your body is more malleable, your muscles rebuild faster. It's also important for runners of all levels to include recovery in their training schedule; just one day per week taken very short and easy, and one week per month taken at about 80% of normal volume (without raising intensity) will be enough to ensure you stay well-recovered.
There is one more component, and that is making sure whatever stresses you add (mileage, intensity, etc.) you add them SLOWLY. If you add them all at once, you add an enormous amount of acute stress, which is highly likely to result in injury. If you add them over a long period of time (at least several months, and some increases should be done over years) the body is actually able to endure a ton of chronic stress (far more than it can handle acutely). This is why a runner doing 30 mpw and bumping it up to 70 is far more likely to get injured than a runner who has consistently been running 80 mpw for a year and bumps up their mileage to 90. The 90 mpw runner is enduring more stress, but their body is adapted to it.
If you add mileage while lowering intensity, your body is more likely to be able to handle it. This is why most runners add mileage after their outdoor season, because they won't have to do intense work for a very long time. However, there is still always a limit, and increased mileage has the strongest correlation with injury of any stress (it also has the strongest correlation with improved times for distance runners, though).
This is a post about injuries I have saved on my computer. The third and fourth sections pertain the most directly to you. I would say a 30 mpw runner going to 100+ all at once would have an insanely high chance of getting injured, and you'd be the luckiest person in the world if you didn't. I would say it's very possible to make a jump like that over a year or two, but you'd pretty much have to completely give up competition during that time. You'd want to keep intensity low and just increase mileage by maybe 5 mpw every month, until you were over 100. Then you could slowly add back intensity.