Comparison-based sorts can only compare pairs of elements. Each comparison has outcomes (less or greater). With possible orderings, you need at least comparisons to distinguish them all.
Stirling's approximation:
So any comparison-based sort needs comparisons in the worst case.
This is a lower bound, not an upper bound. You cannot do better than with comparisons alone.
Escape hatch: Non-comparison sorts (counting sort, radix sort) avoid comparisons entirely. They can achieve when the data has special properties.