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How long did it take the 1st BTC to be mined?
Another nerdy, kinda philosophical, way to answer the question is that it took around 13.787 ± 0.020 billion years.
That's if you take into consideration all that was necessary to have been invented by the time Satoshi could create the genesis block.
The extra 6 days it took to actually mine the first bitcoin then becomes a rounding error at best.