Starting With a Bang!
For me, it depends on the level of familiarity of the players with the system and world as well as their levels.
For lower level characters, or system newbies I like to start slower and ease them into the system and setting instead of immediately tossing them into a lot of combat. They are starting somewhere and they might as well have some sense of what that somewhere is.
If it's a more experienced group, or they are comfortable starting at higher levels, I am more likely to start them up with action sooner than later. I can assume a few things, such as their characters/ players have more worldly knowledge and have been around the block. Their backgrounds might already reflect a lot of the elements of a slower start, so it may not be as needed, or helpful
It's not a hard and fast rule, but it's a place to start. I have also thrown system newbies, who were experienced in other systems into combat immediately and had them do fine. So, ultimately, it's just best to tailor it to your situation. I will typically wait until I have a sense of characters and their general backgrounds/ concepts before planning out an opening scene, though the rest of the game is usually pretty thought through already.
In either case, I like the characters to feel some investment in whatever is happening in the game world, so I spend at least a little time somewhere building some attachment to some part of it, whether it's a stray mutt who always wanders by for scraps, a village where a character lives, or just trading barbs with someone who will become a key antagonist later. I feel that the "getting to know you" will either happen or not in the game and that's more up to the characters than it is to me. I can't force them to talk to each other, just strongly suggest it. :)