By fairly strict definition of TTRPG, there was a D&D-style game released at the very end of the Cold War (Poland, then Russia) called Заколдованная Страна, or "Enchanted Land". Sticking with Poland you can get even a little earlier, but some background first--
I should mention that "official" cultural exports of games past the Iron Wall really didn't happen until the late 1980s, although there were clones. As an example, consider the board game Monopoly. It had a few "unofficial" versions, most notably менеджер (Manager) from 1971 which is pretty close. You can see lots of pictures here of a later edition. The properties you can obtain are restaurants, hotels, theater, transportation, light industry, sports, department stores, and heavy industry.
But even though it was pushed to every corner of the globe by a large company, "official" Monopoly didn't make inroads into the USSR until quite late. There was a Russian version made by Parker Brothers to promote the 1988 World Monopoly Tournament (held in London) and Parker Brothers started negotiations for distribution that same year. When Gorbachev visited in 1990 they made a special commemorative edition in an additional effort to make a deal.
AP News story from June 2, 1990:
Hoping to distribute the game throughout the Soviet Union, Tonka Corp. decorated 1,000 copies of the Russian games with a special seal to commemorate Soviet President Mikhail S. Gorbachev’s visit to Minnesota.
The games are being distributed by the Minnetonka-based firm to visiting Soviet dignitaries and members of the Soviet news media in anticipation of Gorbachev’s arrival Sunday.
The Soviet Union collapsed before any deal could be made.
On top of that, even outside the Eastern Bloc, distribution of Dungeons and Dragons wasn't fast. The first French edition was in 1982, a full eight years after the first English version. Western Germany got theirs in 1983 via the publisher Fantasy-Spiele-Verlag; allegedly the translation job was quite poor. Japan got their first D&D product in 1985 (they got Traveler first, in 1984). The Hebrew version ("Labyrinths and Dragons") didn't start getting translated until 1989. Having to negotiate with the Soviet Union would have added another layer of difficulty; I'm unaware of any effort to make inroads until after the breakup of the USSR.
(Incidentally: the "D&D of Germany" became an entirely different game, Das Schwarze Auge, "The Dark Eye", first published in 1984. If any TTRPG had reached over the into the Eastern Bloc early it'd be that one -- that is, it could have reached East Germany without translation -- but I haven't found any evidence of this happening.)
Now, on to Enchanted Country. I'm afraid I'm not familiar with the Polish version from 1989, but the Russian one from 1990 published by the "Autumn" collective got decent distribution.
The objective, as explained by the game, is to go to a land of dragons, monsters, magicians, and so forth and look for treasures, learn spells, and fight evil sorcerers in castles.
It uses a board, which you can see here as well as cards, which you can see here. There are stats and sometimes rules on the back, something like Magic: the Gathering; here is a sample.
It does have a "game master", and players wander the map with heroes and try to do what clearly resembles standard tabletop-roleplaying, where events get drawn out of the "deck of dangers". There was very little description and the rules were occasionally vague (admittedly, having particular rules being left to the discretion of the game master is not unusual for a table-top game). The leader of the game's booklet includes maps of locations, like this one, which should give a familiar D&D-like feel.
The prime attributes are strength, dexterity, wisdom, courage, and сложение (which I guess best translates to "making" or "building"). The classes are warrior (main attribute strength), elf (strength and courage), magician (wisdom), gnome (dexterity and building prowess), and "Крон" which is sort of a noble (wisdom and dexterity), and there are 12 experience levels.
Of course, this came at the very tail end of the USSR, so there wasn't opportunity for further development past this point.
But I did say, sticking with Poland, you could get a bit earlier. This requires a slightly more expansive notion of what counts; consider the 1979 game Deathmaze designed by Greg Costikyan (famous later for Toon and Paranoia). The game was inspired directly from fantasy role-playing (From the manual: "One idea peculiar to the fantasy role-playing hobby is that of the dungeon. A dungeon is generally a labyrinthine series of catacombs populated by many fantastic creatures.") and involves a dungeon being built up by small chits; there is no game master and the game is allowed to be played solo.
There was an "unofficial" version of this game from Poland, published in 1982!
Jan Adamski had been travelling in Western Europe and "borrowed" some content to publish in Poland (unlike Manager's "re-imagining", this was straightforward plagiarism). He started with Blockade (a game that should be familiar to board game enthusiasts, but is not TTRPG-related) but his second release was Deathmaze. Printing was low quality, and Adamski apparently had terrible trouble distributing his product, but it (and 18 other games) did get out to the Polish gaming public.
Out of all the Eastern Bloc countries, Poland was the ripest for fantasy gaming, and following the Deathmaze clone, through the 1980s there were a number of gamebook "solo RPGs". Various "real" tabletop RPGs were described in magazines but not fully published, and there was an unofficial text file "fan-translation" of the original D&D that showed up around 1990. Even if the government wasn't letting them get the official package, Polish gamers were definitely familiar with table-top RPGs.
...
You can read an interview with Jan Adamski here although note he dances around the idea of plagiarism. There's an in-progress fan conversion of Enchanted Country here intended to be playable on computer, and there are downloads here of pictures including a print-and-play version. Tesera (sort of a Russian version of Boardgamegeek) also has more pictures here.
You can read more about a Polish gamebook entitled Thriller (from 1987) here. (Note that the site supposedly lets you play the game -- it's Internet Archive-only and I wasn't able to get it to work.)
For a book-length and scholarly treatment of "bootleg" gamer shenanigans in the Eastern Bloc (with computer games rather than TTRPGs) I highly recommend:
Švelch, J. (2018). Gaming the Iron Curtain: How Teenagers and Amateurs in Communist Czechoslovakia Claimed the Medium of Computer Games. MIT Press.
In general, no. As other have already written, the trade between the countries on both sides of the 'Iron Curtain' was limited and although there was some exchange carried out by the state-owned industrial and technological companies, generic consumer goods were hard to obtain due to the economic and currency differences between the two systems (with fixed exchange rates being one of the main problems). Thus, the contact with such relatively niche products as the Role-Playing Games was limited to people who could have visited the Western countries to buy the games directly or who had families there and could have received such items via mail (and, of course, possessed linguistic skills to actually make something of the foreign text, as knowledge of English among young people was not really common in 1970s and early 1980s). In addition, very limited access to Western publications meant that relatively few people knew about RPGs and thus there was virtually no coverage, not to mention support for the players.
As others already mentioned, various board games and gamebooks (of Choose Your Own Adventure type) achieved some popularity, and they were either published as unlicensed bootlegs or had their original counterpart made by local authors. The first information concerning actual RPGs started to appear after the first half of the 1980s in magazines for the youth people and in fantasy periodical (e.g. in Poland it were Razem and Fenix, respectively), but these was information that only popularized games, with the actual game material still being largely unavailable.
This changed rapidly in early 1990s, as with the fall of 'Iron Curtain' people started to import various commodities, including publications, giving rise to specialized shops and magazines focusing on the RPGs. One of the first game published in the former Eastern Bloc countries was Czech Dračí doupě (Dragon's Den) heavily influenced by D&D. It should be noted, however, that although D&D is almost synonymous with RPGs in the US, there is no such correlation in Europe, including former communist countries. This was largely due to the fact that in the case of the latter, D&D and by extension, also TSR, being the first game that popularized the entire genre and the first publisher, respectively, gained a hegemonic status on the market, while the market in post-communist countries opened only after D&D got a diverse competition. For example, throughout 1990s and 2000s, the prototypical fantasy RPG in Poland was Warhammer Fantasy Role Play originally published by British company Games Workshop, as this was the first RPG sold as a stand-alone publication and extensively supported in this country. It was, however, predated by Oko Yrrhedesa (Eye of Yrrhedes), written by Andrzej Sapkowski (of Witcher fame) and published in the 'Fenix' magazine, along an article explaining the idea behind Role-Playing Games and already mentioned RPG Kryształy Czasu (Crystals of Time) published periodically in the Magia i Miecz (Sword & Sorcery) magazine since 1992. Being the first stand-alone, comprehensive publication supported by the numerous articles in 'Magia i Miecz' (both translated from White Dwarf under license or written by Polish fans) and add-ons, WFRP gained large popularity. Before the first D&D edition was published in 1995, Polish market already offered local editions of WFRP, Cyberpunk 2020 or Call of Cthulhu as well as several games written by Polish authors. Thus, although already known and further popularized thanks to the video games using (A)D&D rules and world that were published in 1980s and 1990s, Dungeons and Dragons were only one of the games available to Polish player. Situation in Hungary was similar, with the the Túlélők Földje (Land of Survivors), Harc és varázslat (Combat and Sorcery) being published in 1992 with M.A.G.U.S. following in 1993. The latter was also significantly supported by the materials published in Rúna magazine and the novels set in the M.A.G.U.S. world. It is interesting to note, however, that RPGs from the Eastern Bloc countries were almost never translated into other languages and thus their popularity was generally limited to their country of origin.
Last but not least, there was also the financial aspect. The diversity of the original content was not helping, given that publication of numerous add-ons, modules and expansions required substantial money and knowledge of the original material (to select the publication line and make business plan properly) and initially was considered not as attractive as stand-alone games that required only one book to play (today, with the well-functioning economy and increase in the living standards it is not an issue, but for an average player in early-to-mid 1990s it definitely was).
