This is subjective, but I'll describe what you'll probably get if you ask in a Chinese forum, as another perspective.
The UNSC permanent membership may not have directly caused the rapid economic growth, but something related to it may have prevented it from stopping abruptly, like Japan. Of course, there are multiple factors to Japan's problems, if what we intend to discuss is how to solve their problems. But things would be much easier if we just say it's one factor and don't argue which one is more important.
I say "something related to it" because it depends on what you think a UNSC permanent member means. If a random country, say India, suddenly become a permanent member today, without other changes, it won't automatically has this effect. Many would credit the war between China and the fraction under UN's name (and neglect the Koreans, which they would think is less important). Some call it "the first veto" of P.R.China.
Actually this idea is relatively new, and may have appeared after they know more about how westerners think on the internet. For example (quoted from this answer):
Now, there is definitely some controversy over whether the Chinese were bluffing, ... "Memories of Mao Tse-tun's reaction when North Korea was overrun by United Nation troops in 1950 haunted the White House." [quoted from elsewhere] ... Regardless of hypothetical scenarios, ultimately the United States never attempted a ground invasion of North Vietnam. Thus, bluff or genuine promise, China was never confronted with the choice of ...
(No offense to the poster. They are precisely writing what the readers would want and need, and avoided the unnecessary discussions.) So, sadly, friendly arguing based on logical reasons is less effective than the real thing. But fortunately, this is mostly specific to the US, as their theories of politics get lost per president, and may have been rebuilt from "common sense".
Technically, a UNSC permanent member is for preventing something to be done, like how humans deal with things when UN didn't exists. If it directly boosts something positive, instead of preventing something negative, that should mean there is a problem within it. (We all know it has problems anyway, though.)
TL;DR: A general young Chinese would believe power is crucial for surviving after someone else has noticed the development. Not that it directly contributed to the development itself.