Is the belief that the souls of converts to Judaism were present at Mt. Sinai

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based in the Jewish scriptures? Or is it just a common belief with no scriptural basis among some Jews? Not that it makes the belief any less valid.

I hope I worded that correctly. Trying to learn everything I can.
Seriously?
Thanks Kaganate for a more sincere answer. What's a better word than 'scripture' to use? Being raised in a christian church, most of my religious vocabulary is a product of that.