At the risk of sounding like a broken record: when the SHA puzzle is solved is the exact point at which the block which is the input to the SHA is mined. [...] because a point in time is tied to a block of data.I don't get it, so let's try once again. You mine a block, say this [1] one. How is it tied to any particular point in time? It includes a time stamp but that is not the time the block was mined, the block may have been mined before or after that point in time, no way I can tell just from looking at the block.
There is also the hash of the previous block [2] in there but that does not tell my at which point in time the block was mined either. The only thing I can conclude is that the block was mined after the block referenced by the previous block hash but there is no indication of how much time passed in between. And looking at the previous block does not help either because there is nothing in there indicating any point in time.
Or even better, let's do a thought experiment. With a fast enough computer I could have performed all the calculations of the last ten years that led to the Bitcoin block chain as of today within the first hour after the genesis block was mined on January 3rd 2009. Identical to the very last bit. But none of the blocks would have been mined at the same point in time as they were in the actual Bitcoin block chain. I obviously would not have known any of the transactions that would occur over the next ten years but I could of course have guessed them.
Or let's not be that wild and mine the entire Bitcoin block chain within one hour, let's just imagine all the blocks were mined one second earlier than they actually were. This hypothetical Bitcoin block chain could also be identical to the very last bit to the actual one but again none of the corresponding blocks would have been mined at the same point in time. And the fact that two bit-identical block chains could exist but where no two corresponding blocks were mined at the exact same point in time proves that nothing in there ties any block to a specific point in time.
[1] https://blockchain.info/block/0000000000000000001f6d740116db...
[2] https://blockchain.info/block/0000000000000000001a1c88ce0b57...