Quick question, can I buy a game soundtrack on here (in this case https://www.gog.com/game/silence_soundtrack ) and access it without owning the base game?

The page itself doesn't seem to indicate that owning the game itself is required, but wanted to ask first.

No, you need the base game to buy the soundtracks.

You can buy gift codes for them though, but won't be able to redeem it as long as you don't own the base game.

Well if you go to the checkout it says "You have to own SIlence to buy this".. so, no?

Sadly you need base game on GOG to enjoy Soundtrack.
Else you can visit other websites which are specially for game soundtracks.

Long explanation:
The soundtracks are set up as DLC in the store, and in order to register a piece of DLC on your account (ie. purchase for yourself, or redeem from a code), you need to have the base game. You can purchase it as a gift code, but -of course- in order to download it, you need to have it redeemed to your account.

This does make for a (to me) curious situation though - say that a sale makes you notice a game that you hadn't seen before, you figure the base game is worth more than the sale price (I'm probably rather unique in that, yes), but that the sale price seems about right for the DLC's, you can purchase the DLC's as gifts in the sale, and the game itself later. Then you can redeem the DLC's after you've bought the game.

Rather with the developers and publishers, I guess. As far as I can tell soundtracks as DLC started over at Steam. I can imagine that GOG would be willing to sell soundtracks independently if developers and publishers actually expressed interest in such an option. Then again, GOG might have to add a "music" section to the site to limit accidental soundtrack purchases (may sound silly but it's unavoidable that this would happen regularly, particularly to inexperienced gamers, if soundtracks didn't require you to own the game first). I guess there's also a chance that there's some legal mumbo jumbo involved (different laws and taxation for music distribution than games etc.).

Maighstir pretty much explained it already. I too would like to be able to buy the soundtrack to a specific game seperately, though to be honest, I often buy the soundtrack because I experienced it through the game before, anyway. For me it is more annoying when a game doesn't even give you that choice, in those cases where you need to own a specific edition of it to get the OST. When that's the case, or the only available format is only MP3, I check www.bandcamp.com and get it from there instead, if possible.
The page of Tilo Alpermann who did the Silence soundtrack doesn't offer anything related to it, unfortunately:
https://tialp.bandcamp.com/releases
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Edited: Added missing word.

Honestly I think the soundtracks should be purchasable without the game. They don't require the game to run, they are only marked as DLC. So I don't know.

Yep, sad but true, you can't buy them independently. It also goes for Artbooks.

Today I tried buying the Soundtrack + Artbook editions of 2 games (Samorost 3 and The Final Station). I don't own any of the core games in GOG (one I bought elsewhere and the other I've never purchased). At the checkout the "Pay" button was greyed-out and I couldn't finalize the transaction. Only when I removed the 2 items the button became active.
I'd seen the warnings about having to own the core products to "use" the (presumably) MP3s and PDFs, but I thought i'd give it a shot anyway being that logic postulates that you shouldn't need the games to play music and read an e-book. But nope, you do.

The reasons are probably as F4LL0UT mentions in her/his comment, a mix of vestigial DLC dispensation practices spawned at Steam and some tangled copyrighting laws for those other items. I don't know for sure, but those sound to me like good guesses.