Check out GOTM 21. Playing as Greece on a large continents map, with SpaceShip the preferred victory, 132 players turned in winning SpaceShips, ranging from 1170 to 1969 AD. The Spoiler threads for this GOTM will provide some insight on how they played their games.
Large maps require more research per tech, but also allow more space for your civ and more civs to trade techs with. IMO the faster research rate for the smaller maps is to compensate for having less space and fewer civs to trade with.
Buying Techs from the AI is usually cost-effective but you'll never be competitive for an early SpaceShip victory. Better to have 4-turn reseach, trade for Techs the other civs have, and sell to the rest.