It would take everyone a few days to determine the cause, especially the people spreading unverified informations such as 'it was shot down by a missile'
It wouldn't take very long for the relevant parties to know whether they accidentally shot a missile at a 737. For a mechanical issue, there would be much more uncertainty (although it's possible the pilot reported the issue to ATC).
And even then, "ATC, we have a catastrophic engine failure" from the pilots doesn't discount that the catastrophic engine failure was caused by a missile. The pilots don't magically get to know what caused the engine to blow up.