I wouldn't say I think of action and character building as separate things. When I read that people won't care what happens to your characters in an action scene if they don't know them I started to think of a new way to start the story, so that you get to know them first, and then have the action scene that was my opening before.
I suppose I could start that scene earlier and introduce them, but I was looking for advice on a good way to start things off and introduce them. I want to consider my options.
I think you're taking that instruction too literally. It's not about whether your audience has prior familiarity with the characters; it's about whether the action scene has emotional stakes for the reader, whether they care about what's happening to the characters. Sure, it's easier to care about characters they already know, but it's possible to make them care about a new character right off the bat, if you establish that character in a vivid and engaging way or give the audience something about them to identify with.
For instance, just as an example: If you open a scene with a character in a gun battle, don't have her think about locating her opponent and planning her next move or whatever -- have her worry about whether she'll miss her son's piano recital that evening. Or have her be annoyed that she can't get the melody of the enemy's propaganda jingle out of her head. Big or little, give her a concern that the reader can identify with, a goal that she's frustrated in reaching. Everyone can identify with wanting something and being afraid you won't get it. As long as there's something about the character that the reader can connect to and feel empathy for, it doesn't matter whether they knew the character beforehand. They can discover the character in the scene itself as it unfolds.
Often it's not a good idea to put an introduction at the beginning. It can be good to throw the reader in at the deep end and give them bits and pieces of information as they go. If you can make them curious, raise questions that they want to know the answers to, then that's a good hook, because they'll want to keep reading.
I could have them get a distress signal and head to the fight, be doing something off the bridge when they get called to the bridge etc. Any opinions? Anything overdone? Any other options you would like to suggest?
Again, the important thing is to start with something that's relevant to the plot or the character arcs. It doesn't have to be an action scene, but it should be something that has meaning and that gets the audience interested in the characters and their situation.
But if the story
per se begins with responding to a distress call, then that's probably where you want to start, unless the initial off-the-bridge scene sets up something about the characters or the backstory (or even just the theme) that will be important in the story ahead. If you look at a lot of the best stories, moments that seem to be just incidental at the start can turn out to be of great significance later on. One of the most perfectly structured scripts of all time is
Back to the Future, because every single thing that happens in it, even the most casual-seeming moments like Elizabeth writing her note on the clock-tower flyer, has a payoff later in the film. Not one line is wasted.