I wonder if this relates to capitalism vs communism or if it is simply a question of time until anything gets littered with ads.
All I can recall is few absurd billboards like "Fly Aeroflot!" (the only airline) or "Keep your savings in the Sberkassa!" (which probably did not advertise the Sberkassa itself, since it was the only retail bank, but the savings accounts, still looked funny).
There were many airlines (from different countries) flying to and from the USSR.
But you are right, there may be more to it. I couldn't find a period American photo magazine on archive.org. There are old issues of a magazine called "Art Photography"[1], which sounds right, but turns out to be more pornography than photography, so I'm not sure it counts (there are only a few ads, for what it's worth).
On the other hand, popular mechanics is on archive.org ([2], featured previously on HN), and it's chock full of ads; the ads vastly outweigh the editorial content. I guess that's a feature, not a bug: in the 80s and 90s my dad bought computer magazines as much for the ads (ie. as a monthly product catalogue) as for the actual content. Like popular mechanics, they were pretty cheap (PM was 35 cents in 1965, around $2.50 in 2017).
The Soviet Photography magazine could serve as a case study. It wouldn't take forever to tally up the amount of ads in each issue, or even a sample of them. The 89/7 issue had zero ads. One of the last available issues is from around '94[3]. There is a bit of advertising, but not a lot.
The final (outer) page is a full page ad for a Canon EOS 1.
[1] https://archive.org/details/ArtPhotography1952Vol03No08 NSFW, obviously
[2] https://archive.org/details/PopularMechanics1960
[3] https://archive.org/details/sovphoto_v1_1994_02
Edit/PS: I expanded my sample size to 3. The second to last page of a 1975 edition[4] has a full page ad for a Practica LTL[5]. No ads, apart from that.
[4] https://ia801505.us.archive.org/10/items/sovphoto_v1_1975_12...
[5] http://camerapedia.wikia.com/wiki/Praktica_LTL I'm sure the advertised 1.8/50 lens made for fun shooting. Better image quality than an iPhone! Both camera and lens fetch ~50 bucks on ebay, today.
And after posting this ... I am worried FBI or Homeland Security will knock on my door and ship me to Alaska no questions asked.
Companies had ads in various mass media that (a) advertised new products that had been issued; (b) advertised features & proper usage of products (including nudging towards desired behavior) (c) advertised the new styles/designs issued for e.g. clothing. Illustrative product catalogues were a thing. It's a quite different sort of advertising, more like public information and sometimes a bit towards propaganda, but it certainly is advertising.
Also, quite a bit of "traditional" advertising material was made in USSR for export markets.
I would expect any central economic plan to miss consumer needs/desires by a fair margin on a regular basis. Was such advertising also trying to sway consumer behavior back to what the economic planners had original anticipated (as to avoid shortages/surpluses of goods)?
Regarding advertising, the customers of advertisement agencies (there were few in USSR) were firms themselves, not Gosplan. Every Soviet firm or Glavk ("main committee" - sort of a business unit in Soviet government responsible for the management of whole market segment) had a plan, that's true, but it was up to them how to implement it, so some did invest in advertisement (examples were beverages, perfume etc etc).