The chances that “a random human child” will develop mathematical ability (assuming that the culture around her already supports that ability because many people already have the ability) is… dubious. What would be the drive, or the benefit to follow that drive? As a rule, people don’t develop reading ability on their own, and the culture fully supports the ability to read; demands it, even. (Edit to add: Basic reading and writing ability seems to be – to me, anyway – easier by far to learn than the more abstract concepts of mathematics.) And yet we’re covered up with functionally illiterate folks. There isn’t the demand for numerical ability. It’s handy, to be sure! But people can and apparently do function pretty well with next to no computational ability.
But… it’s not impossible, clearly. Two particular (not random) children grew up to independently invent calculus, after all. No one taught them that numerical / computational capability directly, although obviously they had instruction in mathematics that led them to a jumping-off point where it was possible to invent a new means of calculation.
And also obviously, numerical / computational capabilities have been developed “from scratch” over time, as mathematics is an acquired ability, and at one time it simply didn’t exist in any human society. No words for counting, no comprehension of the basic principles of mathematics, calculation, symbolic notation, etc. Those were all invented out of whole cloth by each generation “standing on the shoulders” of the previous generation’s understanding and learning.
So, for a child to be born in the society that @LostInParadise refers to, without even words for numbers, it’s unlikely to the point of impossibility that a child will not only invent a numbering system, the words and concepts for ordering and manipulating these new symbols, nor the language to describe or teach it to others.