I'd hesitate to say that any map is "unwinnable", considering the high levels of skill that some people have, but I definitely think there are certain maps that are "not-worth-bothering-for-someone-of-my-ability". I'm a lousy player, and personally I would not have bothered with that map. I would have junked the game and re-rolled after I found the choke point (or perhaps even before). One of the reasons why I won't play normal Pangaea maps is that they often seem to have such choke points or bottlenecks. I usually only use Hellblazers Pangaea or Acken's version. Acken's certainly has a setting for "smoothness" of the continent, but I don't think the other has.
https://www.reddit.com/r/nqmod/comments/3x319f/hellblazers_maps_pack_now_avaliable/
https://forums.civfanatics.com/thre...-for-singleplayer-and-ai-improvements.550671/
You don't have to install the whole of Acken's mod -- you can just use the maps. The instructions are somewhere on the thread. And incidentally, Consentient recommended using Acken or Hellblazer maps.
I tend to regard the opening of the game as a bit like when you first look at your hand in poker. Sometimes the cards are so bad there is just no point in continuing. This is one of the chance elements in Civ. I've seen at least one video in which a very good player jacked it in after a few moves because it didn't look promising. I'm not a good player, so I need some help, and I not infrequently roll ten maps before I find a start that I like. Sometimes I just can't get a decent map at all and give up. Sometimes when you are playing cards, you don't get a good hand all night. Usually I just look at the tiles I can see on the first move and decide on that. (I want to see decent production, a reasonable amount of food, and two *different* luxuries.) Other times I play twenty moves or more before I give up. But that is just me. Though it is worth noting that the thread for the Deity Challenge Lineup had quite a lot of discussion about maps, and it took some effort for them to produce ones that led to a good game. They not only had to re-roll often, but sometimes took to editing them as well. You might download their maps and look at them to see what a decent start looks like.
One thing that would have discouraged me from playing this map is the shortage of unique luxuries. Neither Sparta nor Corinth seem to have a unique lux, which is bound to cause happiness difficulties. If I had played this map, I think I would probably have settled right on the Marble on the tundra. It's a poor spot in most ways, but it does have the lux and abundant production. The problem is food, and you would need sailing to capitalise on the fish.
Generally speaking, I find being isolated is a real problem. If you can't meet the other Civs it slows down your tech, makes it difficult to trade, makes it difficult to steal workers, and reduces the ability to use diplomacy. If you know one of your neighbours is a warmonger, it is good policy to bribe them to declare war on another neighbour. It can go wrong, because they can end up spreading over the map and eating up cities, but at least it gives you time to arm yourself. Stealing workers is very important because it frees up precious production to build other things. In fact, that is another potent reason why I wouldn't bother with this map. I seem to recall that Peddroelm intimated that if you couldn't steal one or two workers at least, an Honor strategy was not going to work. You only seem to have one worker, and you really need three, if not four. (Old rule of thumb is about 1.5 workers per city.) Consentient advises stealing as many workers as possible. Moreover, having almost no City States nearby makes it problematic to farm experience. I try to steal a worker from a CS that is close enough for me to keep sending archers to it to be shot, then return home to heal. Eventually they get a composite bow or pike and can kill your units, so you have to be careful. Try to learn which turn they are likely to pop out a defensive unit, and change your tactics. On the subject of experience, I play with this mod, which I find handy for judging both the opposition and my own units:
https://forums.civfanatics.com/threads/modmod-thal´s-flagpromotions-for-cpp.547864/
Personally, I don't bother to build catapults. I'd say that at this stage of the game you ought to have six to eight crossbows, perhaps even ten. They dominate at this stage of the game. I'd advise you to re-read Consentient's first few posts in this thread, and make a few notes for yourself that you can refer to during the game. The general pattern is that you build several archers, which you then upgrade to composite bows, which you then upgrade to crossbows, gaining experience all the time. You should have crossbows by about turn 105-110. I would seriously, seriously suggest you watch Acken's China game video (which I think is linked a little above) and any of Peddroelm's videos. It is a real education, which posts like this cannot begin to approach. I was stunned at some of the things I saw them do -- though I still cannot do them myself

Getting experience is important, and getting a ranged unit promoted to logistics makes a huge difference.
My advice? Find a better map, and play the first 100-130 turns and see how you do, then try another map. Learn all the techniques for the opening of the game. The opening is the base for everything that comes afterwards, and it is very difficult to compensate for a poor opening (unless you are playing on the lower levels). If we were chess players I think we would practise different openings, so I don't see why we shouldn't do the same with Civ5. By the way, my timings are based on Deity -- and I would also highly recommend giving Deity a go. Certain aspects of the game, such as worker stealing and trade, are actually easier on Deity, because workers get built faster, and the Civs have more money to give you for horses and iron (I usually sell the lot, because I don't need them at the beginning, and I know I will need the money for upgrades, bribes, and buying City States -- much better to bribe Shaka to go and crush someone else than to have horsemen that will just get killed by him -- and you get a positive diplomatic modifier from having traded recently).
Best of luck with it
