Learn English – The sun will rise even if the rooster doesn’t crow

In my mother tongue, there is an idiom which is roughly translated as:

The sun will rise even if the rooster doesn't crow.

It is a lesson that one shouldn't be arrogant in one's ability, because even though they think that they are doing something important, in reality, it might be something trivial and/or someone else might be even better at doing it. Is there an equivalent (or close enough) idiom in English that I could use?

I want to use it in a story where an rich man refuses to make a contribution to an important social cause, with an air of pomp and arrogance, followed by another character saying something like, "Don't be so arrogant and think that if you don't contribute, this (social cause) won't happen. We will find another way to do it. The sun will rise even if the rooster doesn't crow."

The story behind this idiom is that the rooster observed that the sun always rises after he crows in the morning, and so decided that it was his crowing that made the sun rise. He became arrogant on realising this and decided that if he doesn't get up and crow the next day, the sun won't rise and everyone will beg him to crow. Of course, things did not turn out that way, and his arrogance was shattered the next morning when the sun rose "anyway" and he realised that nobody even noticed that the rooster did not crow.