Depending on how "intro" the conversation is, I'd start "events first" and explain how one can describe a set of events differently. I'd do it with a couple of transparencies, or a sheet of paper (for events and intervals) and one or more transparencies (for systems of coordinates). With your example, draw a Minkowski spacetime diagram with the spatial origin always at Earth, the events of light, neutrinos, and charged particles arriving at the Earth at different times (0 for the light, later for the heavier matter), and the exploded star with the simplification that all the particle occupy exactly same point in spacetime somewhere near the stellar explosion (this is literally a coincidence, in Einsteinian language). Draw in the intervals connecting that point with the points representing the terrestrial detections.

Then start with simply rescaling the coordinates on the timelike axis. Nothing changes but the labels. The same thing if we simply rescale the spacelike axis. We can measure in parsecs, lightyears, lightseconds, metres, and so on; on the time axis we can use seconds or fortnights or kiloyears and the but for the coordinate labels the diagram does not change. Then demonstrate a translation by sliding the timelike axis down so that the timelike origin is last week, last year, next year, and so on; demonstrate a spacelike translation by sliding around the origin on the spacelike axis. Again, invariance is manifest. We can do both types of translation at once, and put the origin on the exploding star instead of on the Earth. All we're changing is the labels associated with the events (and the labels for points along the intervals).

One can also show that a rotation of the coordinates also only changes labels, not relative locations -- this is where a pair of transparencies, or one paper one transparent layer works well. It might be handy to have the rescalings handy on transparencies so you can show that you can freely mix coordinate rescalings and translations and rotations, and the (literal!) underlying picture remains invariant in the face of all of these.

This opens up at least four interesting types of discussion: (1) if we calculate out the light's interval it's 0 (thus "null"). Any segment of the null path from exploded star to detector is also itself lightlike between the two ends of the segment, so dS^2 is still 0. What gives? (Answer: using a set of coordinates lets us deal in coordinate-based distances; and for extra credit we could talk about arbitrary parametrization, affine-parameter style); (2) why are the slopes of the different explosion products different, or why is the interval timelike for the non-light material?; (3) what do boosts do to coordinates?; (4) coordinates representing a moving observer with the origin always fixed on itself leave the underlying picture invariant but suggests kinematics and dynamics; and (5) a contrast between a "conventional" observer that remains at spatial zero but which "evolves" along the timelike axis compared to the same observer against a different set of coordinates.

For extra credit, explicitly distinguish between types of Lagrangian and Eulerian observers that differ only in their choices of systems of coordinates as in (4) and (5), even as the underlying picture of events remains identical for all observers.

This leads us into a block universe picture, where we have (classical or quantum) fields filling the whole of spacetime -- completely everywhere -- with arbitrary sets of coordinates imposed on portions of the spacetime used to describe field-values as (a) "objects" like worldtubes and instantaneous snapshots giving us something like a classical extended object; (b) dynamical laws that in a block universe picture simply predict the field-values (or "objects") at at a coordinate-location in spacetime
given some set of field-values at another location in spacetime [1]; (c) the "conventional" splitting of the block universe into 3+1 spacetime, but showing that the split is as arbitrary as any choice of system of coordinates because we can e.g. rotate a set of Cartesian coordinates differently for relatively boosted "conventional" observers.

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[1] Essentially, this is pulling in the idea that initial values need not be in the relative past for a spacetime-filling IVP solution to obtain! Indeed, undermine the idea that we are evolving initial values in time, rather than extending some set of values outwards from a kernel. Any thought of time evolution can be cured by remembering that one should as a matter of course at least briefly consider all sorts of messed up coordinate charts on top of the underlying block picture. One is simply preferring to work with one static chart for purely personal reasons (which may include the ease with which an intended audience may follow the path to a set of results).

> 1year or 1M years, etc.

Here I would like to believe that "M" means "Martian". Or perhaps "Mercury". :D But those would correspond with a coordinate rescaling rather than a boost.