Not the easiest question, I've wrestled with this a lot for old genre paperbacks. Those mass-market editions from the 70s and 80s can be ghosts. One thing I do is cross-reference with used bookseller catalogs online, like AbeBooks or Biblio. Sellers often list the exact copyright and printing info in their detailed descriptions, especially for collectible editions. It's hit or miss, but you can sometimes piece it together from a few listings.
Another underrated resource is library catalog records. WorldCat is fantastic for this. Search the ISBN if you have it, or the title and author with a specific publisher. The catalog entry often includes the publication year for that precise edition, sourced from library cataloging data, which is usually reliable.
I also keep an eye out for scanned front matter. If someone's selling the book on eBay or Etsy, they might post photos of the copyright page. You can sometimes ask the seller directly for a picture of that page—most are happy to help if they think it'll make a sale. It’s a slower process, but it’s often the only way to confirm a date for a niche reprint.
In the end, it feels like detective work. You’re never 100% sure until you hold the physical copy, but these methods get you close.