As
@DaveC426913 mentioned, it is what was observed.
The first mathematical concept was done by
Buridan, after studying work done a few hundred years before him, who referred to
impetus as being proportional to the weight times the speed. (Not mass and velocity.)
Then, a few centuries later,
Descartes claimed that the total
quantity of motion in the universe is conserved.
Quantity of motion was understood as the product of size and speed. (Again, not mass and velocity.)
A few decades later, Newton finally zeroed in on defining
quantity of motion as "arising from the velocity and quantity of matter conjointly" specifying:
Isaac Newton - Mathematical principles of natural philosophy - Definition I. said:
The quantity of matter is the measure of the same, arising from its density and bulk conjunctly. ... It is this quantity that I mean hereafter everywhere under the name of body or mass. And the same is known by the weight of each body; for it is proportional to the weight.
Which is the modern definition of momentum, i.e. mass times velocity.
I found this info on Wikipedia on pages about
Momentum and
Mass.
So the keyword here is really
observation.