by sheer force of numbers; on the strength of numbers
Fixed expression meaning using numerical superiority to achieve something, often with a nuance of brute force or overwhelming quantity.
They overwhelmed their opponents in one go by sheer force of numbers.
We distributed a huge number of flyers, relying on sheer quantity.
From 数 (numbers) + に (particle) + 物を言わせる (to make something speak, i.e., to bring something into play). The expression literally means 'making numbers speak', i.e., using numerical advantage to achieve a result.