Its complicated. It depends.

A human being has the potential for intelligence. For that to get realized, you need circumstances, you need culture aka "societal" software and the resources to suspend the grind of work in formative years and allow for the speed-running of the process of knowledge preloading before the brain gets stable.

The parents then must support this endeavor under sacrifices.

There is also a ton of chicken-egg catch22s buried in this whole thing.

If the society is not rich then no school, instead childlabour. If child-labour society is pre-industrial ineffective and thus, no riches to support and redistribute.

Also is your societies culture root-hardened. Means - on a collapse of complexity in bad times, can it recover even powering through the usual "redistribute the nuts and bolts from the bakery" sentiments rampant in bad times. Can it stay organize and organize centralizing of funds for new endeavors. Organizing a sailing ship in a medieval society, means in every village 1 person starves to death. Can your society accomplish that without riots?

Thus.

> A human being has the potential for intelligence.

Were we "human" 200.000 years ago the way we are now?

Was the required brain and vocal hardware present?

Of course they were. A human from 200,000 years ago would be almost genetically identical to one from today. That's what makes us homo sapiens. 200,000 years is absolutely nothing on an evolutionary timescale with generations as long as ours and reproduction rates as low as ours.

Yes. Some important parts of the software, like complex tools, art, or the use of symbols only appeared between 100.000 and 50.000 years ago, however.

A human is more then the hardware. A human is hardware with cultural software. A human is decorated with parental education. A human is decorated with local cultural influences. A human inherits his economic circumstances and behavior.

A modern human is a complex artifact and can not be produced everywhere. The ability to cooperate, form institutions and build complex tools may be severely restricted even today. Of course its also restricted in the past.

A human is more then the hardware.

A human is hardware with cultural software.

A human is decorated with parental education.

A human is decorated with local cultural influences.

A human inherits his economic circumstances and behavior.

A modern human is a complex artifact and can not be produced everywhere. The ability to cooperate, form institutions and build complex tools may be severely restricted even today. Of course its also restricted in the past.