First of all the Claymore ETH miner is just a mining software, the actual algo "Dagger Hashimoto" wasn't created by Claymore.

You can't really solve the block in a faster way but you can make your miner more efficient by using less power by saving some functions by skipping steps which aren't required or by using less computations.

However the way the block is hashed is completely random and there is no shortcut, its basically brute force. You have a hash, and you just add a nonce to it a few million times and hope your solution has enough zeros to become a block.
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thank you!
I do not understand computer science but I would love to learn
That made me ask some silly questions
I do not know enough to understand your answer. And still wondering