What does a paramedic do when arriving on the scene?
Check if the patient is breathing.
Check the if the patient is conscious/responsive.
Check for a pulse.
That kind of thing...
Actually, here's an actual EMT checklist but hopefully you get the idea.
What should a performer do when 'arriving on the scene' of a new sight-reading?
Check the key signature.
Check the time signature.
Check the tempo.
Notice the opening notes and the dynamic.
How long should this take? With practice, 2-3 seconds should do the trick.
Let's look at the list a bit more:
Check the key signature.
Actually THINK about what the key signature MEANS. Scan the music for the first note you are likely to miss (usually the last sharp or flat).
For example:
You should immediately look through the music for any C-flats. Really think about the actual slide position. Focus!
Check the time signature.
If you see 6/8, what note will equal the beat, the 8th or the dotted quarter?? Does the time signature change?
Check the tempo.
Hear this tempo in your mind. Hear the first few notes in your head at the right speed. Know what the words mean. Which is faster Andante or Moderato?
Notice the opening notes and the dynamic.
Not only should you notice the opening notes, you can probably "flash memorize" them in your mind. I will sometimes have students try to play the beginning of their sight-reading from memory after having only looked at it for a few seconds. At first they are shocked when I ask them to do this, but you would be surprised at how many notes they can actually process and memorize. I like this trick because it forces them to actually play the music in their minds.
Amazingly, you can train yourself to do this in roughly ten seconds. If you have 30 seconds total to look over a sight-reading example, you can use the remaining seconds to look for tricky section and play them in your mind.
Just like a paramedic, you have a limited amount of time to check those vitals.