Yes, a big nose has been considered a beauty standard in some cultures and historical periods. For example, in Ancient Greece, a prominent nose and small lips were considered attractive features. A round face with a slight double chin was also seen as beautiful.
This standard was likely influenced by the ideal of a strong and healthy physique, as a prominent nose was associated with masculinity and strength. It's important to note that beauty standards vary greatly across cultures and time periods. What is considered beautiful in one culture may not be seen as attractive in another.
Today, Western beauty standards tend to favor smaller noses, but there is a growing movement to embrace diversity and celebrate all types of noses. Many people are challenging the narrow definition of beauty and promoting the idea that everyone is beautiful in their own way.