The nonce is a 64-bit unsigned integer. The nonce is the solution to the puzzle. A miner keeps incrementing the nonce until it finds the solution. Now you must be wondering if there is a miner who has hash power more than any other miner in the network, would the miner always find nonce first? Well, it wouldn't.
The hash of the block that the miners are mining is different for every miner because the hash depends on things such as the timestamp, miner address, and so on, and it's unlikely that it will be the same for all miners. Therefore, it's not a race to solve the puzzle; rather, it's a lottery system. But of course, a miner is likely to get lucky depending on its hash power, but that doesn't mean the miner will always find the next block.