This has probably been talked about before, but when you want to start making a backup library of your games there is really no official way of being certain of the file integrity after the backup.
The only way to do it is to start the installer with the file integrity check, but this is extremely impractical, especially if you have many games or are making multiple redundant backups. It also makes ROM backups, like M-Disc backups, risky.

Ideally we need checksums,
It would also help tremendously if we could run the installer's file integrity check without have to start the actual install of the game.

They should show that info next to download links in user libraries...

In the meantime, the more inconvenient way is to go to download history in your browser, copy link to the installer file you downloaded, add .xml at the very end of the copied URL (so it would end with .exe.xml for example) and hit Enter.
Or you could look into gogrepo.py user script, I think it provides an option to check MD5 sums (but I'm not completely sure about that).

Yeah, it's almost as if GOG Galaxy replaced a far simpler, and far more useful Downloader tool.

It does.
https://www.gog.com/forum/general/gogrepopy_for_dummies_helpful_hints_for_total_noobs/post5

I have been backing up games for years now, but I have only used the integrity check when installing GOG games and FastCopy when transferring files to another hard drive. I’ve never had any issues with this method.

Whenever I download an offline installer, I always install it to ensure it works correctly. When it comes to creating multiple backups, I use FastCopy to transfer/verify that the installers transfer over properly.

Note: I do use galaxy for downloading installers which I think check the file integrity. Correct me if I'm wrong.

Isn't there a command line switch you can throw at the installers?

That's how I do it for all my archiving, and I also save those xmls with my downloaded files for future reference. Yes, it contains extraneous data too, but that's just me being a tad lazy.

You've probably been lucky then. I personally use the superior TeraCopy for file copying and moving. It supposedly does or should, because the MD5 checksum values are available in the GOG SDK. They exist, just not in a user friendly manner.

You need to use Galaxy or a third party program like gogcli.exe or gorepo.py etc, which obtain the MD5 checksum values from the GOG SDK.

Another slower method, akin to installing, is to use InnoExtract in test mode. It is a free program and a bit faster than installing. It takes a while to complete though, as it checks the integrity of every file inside your EXE and BIN file packages. GOG use InnoSetup for their installers.

I created a GUI for InnoExtract (and 7-Zip etc) some time ago, to make that simpler, called GOGPlus Download Checker, available at GitHub.

There is an old thread of mine about it - https://www.gog.com/forum/general/gogplus_download_checker
Just don't get confused with the other programs on offer in that thread.

I have been backing up games since I started using GOG, and I haven't encountered any issues. When I first began backing up, I wasn't even using TeraCopy or FastCopy. Despite having backed up almost 2,000 games, I've had no problems at all. I also have a 4TB hard drive that has several hundred games installed for me to play on my PC. I'm constantly testing my games.

But hey if I'm lucky I'll take it.

I initially used TeraCopy, but I found it slower compared to FastCopy and to much resource hog. That's why I prefer FastCopy for its lightweight and simple interface, although TeraCopy is still quite good.

I've been mostly lucky too, and have many 4TB drives, and some larger and smaller, to backup up multiple copies of my GOG games and a bunch of DRM-Free games from other sources. I've gotten over 2,000 games (etc) from GOG now, plus many hundred games (if not thousands) from other stores.

The majority of testing I have done, has been with the GOG SDK checksum values and file size values, plus testing the zip files with 7-Zip. When that hasn't been an option, I have used InnoExtract in test mode, plus 7-Zip for Linux and Mac version files. I also use InnoExtract etc with Itch.io games, and those from ZOOM Platform, Humble and IndieGala, etc. I view TeraCopy as superior because of its integration options, and not going too fast makes me feel it is more reliable. Speed is not everything. In fact, I built my own frontend for TeraCopy, called TeraCopy Cure, to address some of its issues and limitations. It ensures copy and move jobs happen in the order they should, plus you can set a timer value for each job, before it starts. All part of my 'be nice to hard drives to make them last longer and be more reliable philosophy'. I've been using TeraCopy (free version) for well over a decade now. And even though I see it as superior, it has some issues, hence why I've never paid for the full version. In fact, annoyance drove me to create my frontend GUI for it.

If you're able to make use of checksums, then surely you are capable of generating them yourself? Or even better, something like PAR2. Of course you need to initially verify that the file is uncorrupted, but I'm assuming that you install and play everything you buy at some point, so you can generate the checksums after the installer has verified itself.

With backlogs as they are, installing and playing may come years after downloading, if ever in some cases, while the need to verify comes the moment you download and want to make sure you keep a good installer.

all you need is a delta checker and a hash file for each game.
if done correctly it can even repair broken hives.

Personally I don't buy anything until I want to play it, as it would be a waste of space backing up something that I'm not even sure will be worth playing. However you can just create a checksum when you download it regardless. The only way that would fail is in the very unlikely case that the file was corrupt when you downloaded it and it was no longer available to download by the time you actually played it. Or install it immediately just for testing purposes. It's only once per game, so it's not a huge burden.

In that case, you may be surprised to find that you're in a pretty small minority...
Checking that the download wasn't corrupted is the main point of this request...
There are people with thousands of games, and many more with several hundred, and even for fewer, just installing and then immediately uninstalling is an unnecessary complication, and if you want to really clean up after and keep the system tidy it may quite a while. And with the increasing size of games, all of those pointless writes may take a non-negligible toll on the lifespan of SSDs. But beyond all that, many games may be unplayable on your current computer, being purchased for later, and some may even be uninstallable, mainly due to the OS. Or simply the lack of space, especially considering that GOG's installers first unpack everything in Temp.

It should be a very simple thing. GOG has those checksums, they should just list them. What the OP said, offering the option of just checking integrity with the installer without actually installing, would be an added bonus.