In essence, the idea of us being among the first in our galaxy is compatible with the notion that intelligent life forming is so scarce that there's only ever going to be just a couple civilizations in our galaxy or that we're alone; because if life is so common that our galaxy would have (for example) a hundred intelligent civilization spawning events, then the expectation is that half of them would have been before us, and it would be a really, really unlikely that all of them are on Earth-like planets younger than us and none of them are on the multitude of Earth-like planets orbiting Sun-like planets older than us.
Also, given all the time-consuming steps required for life to form, "around the same time" would optimistically mean something on the scale of +/- a million years. Like, if the protozoic era took 0.1% more or less, that would be a difference of two million years; so if some civilization was much older or much younger, then the difference would be much more than that, and if we encounter a planet that's +/- hundred thousand years of progress, that mean that we really progressed at a remarkably coincidentally equal starting point and pace; and if we encounter a civilization that's just a thousand years of technological development ahead or behind, then that would be a so unbelievable coincidence that I'd consider that some kind of intelligent designer is required to explain it.
The concept of simultaneous discovery happens because the discoverers share an environment where the prerequisites for that discovery appear at the same time; this would not be plausible for civilizations forming naturally through evolution without any contact or influence between them, that would work only if they're e.g. intentionally designed and "planted" on planets by some previous civilization.
