That used to be possible in civ 4 where that is the early rush of a civilization where other civilizations didn't know and you didn't receive the "You declared war on our friend." penalty. However, in civ 5, whenever you conquer a city, there is a warning before you capture a city where it'll tell you whether you get a warmongering penalty. Whether it is a major warmongering bonus or a minor warmongering bonus depending on the city.
The penalties apply only to the Civs you've already met. You meet a Civ one turn after you captured a city and they won't know.
What can affect them, though, is if you get denounced as a result of warmongering (or anything else beside). The denouncement will affect their view of you until it's no longer in effect (but they won't know why, so they won't add any warmongering penalty to that), and when you meet a new Civ you don't yet have positive relation modifiers to mitigate the denouncement, so this might affect you very badly (not getting deals with the new Civ, or even get denounced early), thus the idea of the previous poster to wipe out all civs on his continent/island before he meets anyone else. Denouncements made by dead Civs don't affect anyone.
For e.g. I think the devs had in mind the Mongols could now be played this way (which will work only on specific maps, and it wouldn't be an easy strategy to play) and that isn't far from the historical Civ (early rush of conquest to expand, followed by peace and stability, and encouraging foreign friendships and trade. It's wide, with settling as much and early conquest instead):
Small continents might work best as on archipelago the risk is high to have a lot of neighbors reachable by trireme and scouts than can cross one tile of water to you as early as Optics:
- You don't explore by sea early on. You want to avoid discovering off continent neighbors early. If your neighbors have triremes, you kill those ships to stop them from exploring. Better yet, you deal with their coastal cities as a priority and raze them. No one without Optics at worse and maybe Astronomy if you're lucky will be able to discover you before you want to be discovered.
- You start conquering early (also getting cities via peace treaties to accelerate matters), favoring cities with unique luxuries, razing those that bring nothing at this point (you can resettle there later once you control the land and have raised your happiness enough) never neglecting to upgrade luxuries. You send TR to CS for gold, or you bully them. You build all happiness buildings or pick happiness beliefs.
- If you have one neighbor to conquer, you finish him off. If you've got 2-3, you try to finish at least two off if they denounced you (to avoid 2 denouncers influencing one another and creating a loop of denouncements), or you get powerful enough to intimidate them so they won't dare denounce you a second time (their first denouncement should stop having effects by the time you'll explore and discover other Civs). This way your early warmongering won't have any lasting diplo effect. You can conquer or not the city states nearby, depending if you need them more as allies and for TR than you might benefit from the cities (you can even keep them for last, if coastal they may become your coastal cities/trade hubs when you're ready to open up to the world). You can very well get screwed if you have many other Civs than can reach you very early, then you have to adapt and change strategy depending on when it happened and how bad your diplo is.
Once (if!) your "big empire" is on the tracks, you assign your caravans internally for growth, start catching up on infrastucture you neglected in favor of units to conquer, start exploration, try to meet many CS and Civs, get your economy in better shape and start increasing your happiness with trade deals (you should have many extra resources), alliances with Mercantile CS, finish to settle your land. Then you switch to a peaceful wide game, or for a long-ish peace while you slowly prepare to launch a Domination campaign.
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