I'm not sure I'll be playing this month. RL is getting busy. Hopefully I'll end up with time later in the month. It is after all just a small map
I don't think that enough is known about the map to make firm plans. It will be very important on this map to be opportunistic, watching for potential advantages and adapting as things evolve.
I do have some general thoughts, most of them subject to change depending on how things unfold. The geography will have an especially strong effect. Many of my thoughts are based on the assumption that most Civs will be in contact at a fairly early date. That seems most likely to me. But it is possible that we're somewhat isolated at the start and in that case a lot of the following would change a bit. Another thing which will have a strong impact is the availability of resources. Impossible to guess in advance whether early aggression is something I'll try, that decision will have to wait until more is known.
Seven rivals on a small map is likely to be a bit crowded. Unless there's something about the geography which precludes this I'd expect some early wars.
The tech pace will be fast. If most AIs have contact early on then the early game tech pace will be very fast. If we contribute to it with aggressive trading and research the tech pace will be extremely fast. But I do think it will be possible for us to remain competitive in research. Expanding as quickly as possible at the start will be important of course to build up some capacity. I think it will be possible to build the Great Library to catch up early techs - I'll write more about that possibility further down. I don't plan to try that, expect I will trade and research for tech.
I don't think this will be a good map for my more usual style of falling behind in tech at the start and catching up later. The value of the trades I like to make when Writing and MapMaking become available could be low on this map. (Depending a bit on geography, the small map means the AIs will have explored more and have more contacts, resulting in less for me to trade.) Combined with the high pace I think this means that casually falling behind in tech will not work well. I'll make an effort to stay caught up in tech on this one.
I don't plan to try it but it may be possible to get a tech via forty turn research and then leverage it in trading. It will be a bit of a gamble. If trying for this I think the best candidate for it will be Polytheism. In any case for this to work it will be important to get the prerequisite techs as soon as any other Civs know them and to start the forty turns asap to maximize the chance of success.
This could be an ideal map for a Palace jump. Forbidden Palace can be built after just seven towns. If there's a bit of expansion room and it is possible to found a good city for the new Palace early on, a peaceful Palace jump could work well. Definitely a possibility to watch for and to take if it seems appropriate.
Wonders: It will be difficult to build any early wonders in this game. The AIs have their Emperor advantage, and the fast tech pace means there will be more wonder cascades. I think it will be possible to build the Great Library but only by dedicating major effort to it. I don't plan to try it. If you do go for this I'd suggest: 1) Start a prebuild around 3000BC (not much later!) in one of your first two towns. 2) Groom that town's production - ensure that the tiles its citizens are working are productive, that there is no unrest there, and that it continues to grow at a good pace. 3) Going for Great Library may be incompatible with going for a Palace jump.
Temples: I plan to build very few, perhaps none. If there's a severe luxury shortage I might change my mind on this in a few towns. Literature should be known fairly early in the game. Due to the high tech pace it won't be possible to build all improvements in all towns. Libraries are a cheaper way for us (as a scientific Civ) to maintain cultural parity than temples, and they'll boost our research capacity at the same time.
Golden Age: The Sipahi will be available a bit later than I'd like for a Golden Age. But I think they're the way I'll plan to trigger it. The alternative by building wonders doesn't look good in this game. Our traits mean that for an earlier Golden Age we'd need to build the Great Library and any one of the Great Wall, Hanging Gardens, or Pyramids. It will be tough to meet those conditions on this map. If we can capture one of the required wonders that could change things. Probably not though.
I'm still mulling over opening moves. Where we are in the minimap might have some influence. My current thinking is:
1) Rapid expansion is even more important than usual since the map is likely to be crowded.
2) Unless the start position is extremely crowded, or there turn out to be some nice food bonuses nearby, I'll want a granary. It would be a pity to build Granary in the capital and then abandon it in a Palace jump later on but I'll do that if it seems best, i.e. if there's no food bonus for the capital.
3) First move the warrior to the eastern mountain. That will expose a number of tiles which look like a grassland area. If a food bonus is revealed then all other bets are off, my worker and settler will move to take advantage of it.
4) If no food bonus from (1) then move the worker to the northern mountain to reveal as many other tiles as possible. Again, if a food bonus becomes visible then that will dictate my subsequent moves.
5) If no food bonus from either (1) or (2) then it will be tempting to throw the dice and move the settler west or south to continue the search. I may throw some dice to decide

Probably not, probably settle at the start. And then start by researching Pottery and building a Granary immediately. Even with two wasted worker moves it will be possible to build the Granary before the capital grows to size three, and then produce the first settler a few turns after that growth.