There are two different delays at work. One is the 5.5 billion years between when an event happened and when the signal reaches Earth; the other is the weeks/months/years delay between when the first part of the signal reaches Earth and when that signal is appreciated for what it is.
In this case, we are ignoring the first delay and only talking about reducing the second one. The event happened 5.5 billion years ago, and nothing is changing that.
The thing about astronomy is that we take many, many photographs of different parts of the sky every night, in all different wavelengths. Usually any given project is just looking for certain things (large elliptical galaxies, planets around Sun-like stars, comets, etc.), and that's all the data is initially used for. We can't analyze every byte of data for every possible scientific goal, if for no other reason than we don't have an exhaustive list of what to even look for.
But we try not to throw away this data (to an extent; storage isn't free after all). So people can later look at data sets with new criteria for what counts as scientifically noteworthy. Bursts similar to the one in question are often found in this review process.
If instead one looks for bursts "in real time" -- identifying them as soon as the data is gathered -- one can look at the event with other telescopes in other wavelengths, to get a more complete picture of what is happening. (No one telescope can ever see more than a small fraction of the electromagnetic spectrum.) Once the burst has completely faded, it's too late to try to gather more data on it.