If the universe had started to collapse within the last 10 million years, we would have seen a slight cosmological 'blue shift' in the light from nearby galaxies. If collapse had begun within the last billion years, all the galaxies within 1 billion light years would show a cosmological blue shift not a red shift. Galaxies more distant than 1 billion light years would, however, show a redshift because at a time more than 1 billion years ago, galaxies were still expanding away from us. So, I would venture to say that it would be hard for the universe to fool is by collapsing without our noticing.