In this block
https://www.blockchain.com/btc/block/000000000000000000024b00ee235c122bde60104462bb41396428af892bf9acthe Nonce is 3,564,549,738 which isn't a very large number.
I thought proof of work required miners to find a nonce that when added to the block data, produced a block hash of something beginning with a string of zeros.
If I started with a nonce of 1 and tried hashing 1,2,3,5...3,564,549,738 - that would not take much work at all.
Obviously I am completely misunderstanding something, as all the nonces on recent blocks are fairly small
You are not fully misunderstanding. There are extra nonces, as BlackHatCoiner mentioned. However, timestamp is not enough anymore, and miners also added coinbase transaction as an extra nonce.
I was able to find something about it in Mastering Bitcoin book.
https://www.oreilly.com/library/view/mastering-bitcoin/9781491902639/ch08.htmlIn the genesis block, for example, Satoshi Nakamoto added the text “The Times 03/Jan/2009 Chancellor on brink of second bailout for banks” in the coinbase data, using it as a proof of the date and to convey a message. Currently, miners use the coinbase data to include extra nonce values and strings identifying the mining pool, as we will see in the following sections.
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The next few hexadecimal digits (03858402062) are used to encode an extra nonce (see The Extra Nonce Solution), or random value, used to find a suitable proof of work solution.
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The Extra Nonce Solution
Since 2012, bitcoin mining has evolved to resolve a fundamental limitation in the structure of the block header. In the early days of bitcoin, a miner could find a block by iterating through the nonce until the resulting hash was below the target. As difficulty increased, miners often cycled through all 4 billion values of the nonce without finding a block. However, this was easily resolved by updating the block timestamp to account for the elapsed time. Because the timestamp is part of the header, the change would allow miners to iterate through the values of the nonce again with different results. Once mining hardware exceeded 4 GH/sec, however, this approach became increasingly difficult because the nonce values were exhausted in less than a second. As ASIC mining equipment started pushing and then exceeding the TH/sec hash rate, the mining software needed more space for nonce values in order to find valid blocks. The timestamp could be stretched a bit, but moving it too far into the future would cause the block to become invalid. A new source of “change” was needed in the block header. The solution was to use the coinbase transaction as a source of extra nonce values. Because the coinbase script can store between 2 and 100 bytes of data, miners started using that space as extra nonce space, allowing them to explore a much larger range of block header values to find valid blocks. The coinbase transaction is included in the merkle tree, which means that any change in the coinbase script causes the merkle root to change. Eight bytes of extra nonce, plus the 4 bytes of “standard” nonce allow miners to explore a total 296 (8 followed by 28 zeros) possibilities per second without having to modify the timestamp. If, in the future, miners could run through all these possibilities, they could then modify the timestamp. There is also more space in the coinbase script for future expansion of the extra nonce space.
As mentioned in the above text, miners will be able to create even more variables as "extra nonce" as difficult increases in the coinbase script.
I made a quick summary on PoW
here