Simple & Direct:
* The universe exists.
* Life exists on Earth.
* My doubts still exist.
More nuanced:
* The question of whether or not God exists has been debated for centuries.
* Despite the hardships, hope still exists.
* To truly exist is to live with purpose.
Figurative:
* The rumors of his disappearance simply do not exist.
* My fear of failure exists only in my mind.
* The world they lived in exists only in their imagination.
Ultimately, the best sentence to use will depend on the specific context you are discussing.