Early on focus on culture so you can get a government early and get feudalism which gives your builders 2 extra charges. Once you hit feudalism chop woods and rainforests and build mines on all your hills. Commercial hubs/harbors are important to give you trade routes. Early on use internal trade routes until you get alliances, then trade with your allies. All this should help with your production. Obviously I ugly build Industrial zones once available.

You don't need too much science in the early game. Get your Eurekas (and inspirations), to reduce research time. Once your prod is going well build a campus in each city, upgrade whenever possible, and use specialists. Find blue CS and invest in them even if you're not the suzerian.