You did not specify how hard the "not guessable" requirement is. Of course you would not use simple serial numbers, but I would not rule out a mechanism that can create unique strings using simple cryptographic techniques and does not need a database at all.
What are the IDs used for? Just identification of an item? Or are they used as some kind of license key or access token?
What is at stake? What damage happens when an ID is guessed? With millions of products per day, I don't assume that the value of each is in the hundreds of dollars (if it were, your customer would pay an expert who wouldn't ask on stack exchange :-) )
What level of adversaries do you expect? Ordinary users, script kiddies, determined hackers, state-level actors?
What profit can they gain, i.e. what amount of effort would they invest to hack your scheme?
If there is a real risk of being hacked and the possible damage is high, this scheme is probably too simple, but from the limited information you provide, I don't think so.
10 alphanumeric characters give roughly 60 bits (if you use uppercase, lowercase and digits). That's close enough to 64 that a 64-bit block cipher could be used here. So you start with just sequential numbers and encrypt them using a 64-bit block cipher (and a key that needs to be kept secret, of course), skipping those numbers which result in out-of-bounds encrypted values - on average, every 24th number is good.
Since the block encryption is reversible, the resulting bit patterns are unique, and you can safely use them without storing them anywhere. By decrypting a given ID, you can verify that it was generated using your algorithm and key (if the decrypted value is less than the current value of the generator, it was created by this algorithm.) If you store just the last value of the sequence number generator for each day, you can even determine on which day a key was generated.
Of course, once your algorithm and the block cipher being used is known, breaking the key requires "just" a number of IDs known to be sequential, and enough time and computation power. State level actors could probably do this, I'm not sure about determined hackers.