Oh yes.. the Buddha is omnipresent/all pervading in everywhere
and everything and is our true nature.. called Buddha Nature. Even
grass, trees, have this Dharma Nature (in inanimate things we call
'Dharma Nature', in animate things we call 'Buddha Nature'). It is
the pristine awareness that is everpresent, everlasting, without
which nothing would "exist".. it is like a mirror that never stops
reflecting. Because our true nature is one with Buddhas, we, the
universe, are one without separation, and there is no separation
called 'you', 'me', etc. These are appearances due to dualistic
discriminations.
Our Buddha Nature is also all-encompassing and space-like. For
example when you pour water into a space in a cup, this space will
not reject the water. At the same time this space is not
diminished. Without Buddha Nature, Planet Earth cannot be in the
space. Cars cannot works. Every thing is benefited by Buddha
Nature. Enlightened people recognises it/lives in this reality all
the time.
And this is not just a theory. It is not impossible to awaken to
this truth intuively, directly, in fact, other than my dharma
teachers and uncountable practitioners and masters in the world,
quite a few people in this forum already has seen for himself that
Buddha Nature is real, is our true essence. The goal of Buddhism is
to 'ming xin jian xing' - to see one's true nature. If we practise
earnestly, we will be able to 'achieve' that.