This is worse asked as "how do we know variability exists". A variable is an intuitive concept, although it's full technical description is not necessary for a primary / elementary school child to learn how to use variables in function space.

We have dependent variables and independent variables, and clearly it means that which can be varied, but what creates variability?

In some descriptions of mathematics you'll find there is explained this idea that the null set is the basis of numeration, but 0 was invented long after numeration had transitioned from being invented to being discovered.

"A variable is a symbol for a number that is liable to change"

Yes, but what creates the variable? What allows for us to know this is a mathematically sound idea?

I learnt variables in grade 4, but I'd like to relearn them as a 4th year.

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