That's not how prestige works.
For example Ivy League Universities are considered among some of the most prestigious universities on earth not bcuz those Universities think themselves prestigious but bcuz they have earned respect in the world by producing some of the best scholars, carrying out world class research, etc.
In short prestige doesn't come from a nation thinking highly of itself instead it stems from the rest of the world holding that nation/country in high regard.
So plz elaborate again on how joining the NSG would somehow bring prestige.