mining theory – At what point in the block do bitcoin miners start finding the nonce to solve the puzzle?


Do all miners coordinate and start solving the puzzle at once(Like x mins from last blocks transaction added to the block or min limit on a number of transactions)?
In case there are no constraints on when miners can start solving the puzzle. Can’t a miner start finding nonce after he adds one transaction to the block ignoring all new transactions? This way he could increase the chance of incentives.

I feel my understanding seems too wrong as the possibility of this scenario could lead the whole network to be greedy. It would be great if someone clarifies this.

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