The amount of these things available initially seems to be based on a random seed. You definitely do NOT need to play a smaller map to get more of these. I play exclusively large maps (and I'm looking forward to even larger maps in the future). Some new games are absolutely loaded with goodies/events, and others are spread much further out. I'd just suggest reloading if the map doesn't look promising from the start.
You can also increase the number of these goodies/events by researching Adventurer Tech tree. At the moment this is the first thing I do when i start a new game, as I really enjoy leveling up and equipping my heroes from them while the city builds. With a bit of luck, you can get 2-3 levels in this in the first 30 or so turns and have plenty of events to keep you busy 
Eventually I'm sure we will get an option to be able to adjust this at game creation (Like in GalCiv 2), but for the moment you can either just reload until you get a good variety, or until you get a lost tech temple so you can rush through the adventure tech line.
I'm currently lucky and playing a game where both occurred, and I can't even clear things fast enough. It almost feels more like a game of HoMM and I've totally neglected my city/civ building, but I'm still having a blast (and making far more gold than I can spend at this point).
Each game is different, and that is one of the great things about this and gal civ 2. There are some games where you get lots of empty space, and others with virtually none. They typically play very differently and help to give great re playability to the game. Eventually I'm sure we will have the options to specify exactly what type of game we want, but for now there is always the new game option if your looking for a specific type of game.