First, you don't have to be the biggest one. Being stuck at 4 cities is very bad for you, but you don't have to have the most cities, this is not Civ3.
Note how Huge maps are intended for more than 8 civs - as a result, every civ on this map will be larger than you would otherwise expect.
Overall, I find that lebensraum wars are quite necessary sometimes, and they're very often useful. Generally, I go and beat up on one civ in the early game, maybe not completely destroying them, but getting myself more room. Which civ? Well, of course, your geography is important here. However, if you have a choice, it's better to fight a civ that you'd probably end up at war with anyway. Genghis Khan or Montezuma are aggressive and are thus good candidates for a war; someone like Mansa Musa or Gandhi could end up being a very good trading partner if you don't fight, though.
Your problem actually probably lies elsewhere, not with expansion. You should be able to get pretty far ahead of Noble civs in research - build cottages. Cottages are awesome. Through good use of cottages you can, in fact, be pretty good in the tech race on Monarch, even.