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Only if you have trusted the right person to give you the correct genesis block.

In the case of bitcoin, I don't believe anyone could mine their own genesis block and build a chain even remotely approaching the length of the "standard" bitcoin chain. In fact, this applies more generally: after a blockchain has been in existence even a short time, it becomes infeasible for anyone to replace it entirely; at best they can hope to produce a fork from a fairly recent point as anything else would be a DRASTICALLY shorter chain.

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