What was the earliest time that conversion from sugar beet to sugar can be invented?

I doubt it. I'll have to check if there is any genetic research on that, but the conventional view last I checked is that sugar beets are the result of long selective breeding for sweetness and did not have enough sugar content to be noticeably sweeter than other vegetables before the sixteenth century. So, assuming we have good success with the process, I'd say early to mid seventeenth century.
 
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