In a prior life so-to-speak, I was a public securities analyst for 9 years. The information that you think that you need is indeed rarely available in direct form, but reasonable proxies can be derived from the information that typically is available.
There are special circumstances such as regulated industries or small-volume industries where the unit volumes must be explicitly disclosed.
The most likely source of "direct" numbers (i.e. unit volumes) would be reports by industry analyst (i.e. the type that sells their services and data to companies, such as say, the Gartner group). To be clear, they would have done the "hard-work" for you, but the numbers that they have are most likely derived.
With that said, getting unit-volume numbers is pretty much what you would expect. An analytical drill of breaking down gross revenues (and COGS) into the components, making reasonable assumptions for unit cost, and dividing. There are some secondary tricks that can be used, such as triangulating differential data between periods (e.g. quarter to quarter), or simply tearing into press releases where often such numbers are citied or "between the lines", or promotional information from competitors (e.g. where they say that they're #2 at such and such a volume, wherein obviously that implies that the gross volume is at least twice that, and so on).
Having said that, the calibre / significance of these derived numbers are typically more than sufficient for business purposes that I envision that you need. For example, I expect and would hope that being off by a factor of 2, doesn't make or break your business or business case (if it does, then there's bigger problems). This includes planning inventory and facilities. Similarly, a key part of any new business is market-growth - unit volume that literally doesn't exist now, but is actually spurred by the startup itself. Even winging-it is often sufficient... there's x-billion of people that would buy this shirt at this price level; 10% penetration is this volume and we expect that our product will expand the market from x-billion to y-billion. I'm responding abstractly because that's all I've got to work with from you question. My point being that unless there's some business issue that's very decisive on knowing the hard gross unit-volumes, and as one who has suffered extracting and using such details, I expect that some simple anecdotally inferred numbers would be sufficient.