Civ in general, and VP in particular, is a game about long-term planning. On occasion you may get a strong advantage in Classical, but usually you'll stay behind or on par with the stronger AIs for the first few eras. That goes double for harder difficulties. And that's okay - as long as you hold on and don't give up, each era will give you new ways to catch up, and then you will be able to execute your long-term plan.
As for Poland specifically, I played a Domination game with them a few months ago. Here are my thoughts regarding this civ:
1 - People call Poland a generalist civ and I can see what they mean, but personally I find them very well-suited for Domination, as many of their components (even the UA, indirectly) are helpful for that. If Progress hasn't worked out for you, try starting with Authority - it has more production and better potential for culture gain.
2 - What is the long-term plan? For Poland, I'd say it is to focus on culture income and overtake the other civs on policies by a mile. This happens incrementally, and the biggest gain is around Industrial - you'll get an Ideology with multiple tenets while other civs haven't even finished their normal policy trees, so this is an ideal time to leverage your advantage to the fullest.
3 - With a long-term plan done, you need to figure out how to get there. For Ancient/Classical, focus on founding and consolidating your main cities, build up a basic army for defense, and get your Authority culture by hunting barbs diligently. Since we don't have many tools for warmongering yet, don't attack other civs unless you know they're vulnerable. (If they attack you instead, that's actually a bit better for you, because it's easier to kill their units near your territory where you have healing and city support. Just don't let them pillage too much, and get those kills for the yields.) As for religion, you don't have much going for it, so losing the founding race is possible; that said, one advantage of playing for Domination is that you can conquer someone else's religion for yourself, if you don't found. Take it easy and don't sweat it if you haven't got the perfect religion.
4- The Medieval age is where things start to get good with the Ducal Stable. It has strong yields, an XP bonus, and free horses to give you a strategic monopoly and a large army of mounted units. It's ideal to start building your offensive forces once your stables/armories are online, then engage in a few wars against your neighbors, and maybe vassalize someone if you can (get friends to help you in war whenever possible). If you're playing with 4UCs, your extra two components also come online during this age and are pretty useful as well.
5 - Renaissance gives you a LOT of new tools to overcome the AIs. You get: a free policy from your UA; a spy, which you can use to catch up on tech; the World Congress; and Winged Hussars, a VERY strong unit that can carry entire wars by itself. Make as many of them as possible, combine them with some other key units (siege, naval, some land ranged support), and use these advantages to play more aggressively.
6 - Industrial is where your long-term plan comes to fruition. If everything was done correctly, you should have a large and well-trained army, some civs already defeated/vassalized, and a jump-start on your Ideology, while everyone else is unable to catch up to you on culture. Continue using spies to get science from other civs, and leverage your ideology to get whatever you need to close out the game. Of course, don't neglect implementing new tools as they become available - factories and industrial connections for a breakthrough in production, corporations in the Modern age, etc.
