We shouldn't deny the 'existence' of these problems. [=we shouldn't deny that these problems are present or real]
long before the country had 'come into existence' [=begun to exist; come to have actual being]
I owe my very 'existence' [='life'] to their courage. [=I am alive because of their courage]
(..) -Dead? Sort of. He works at the post office. No. If Serleena gets to Kay before we do, he's dead. The Earth's very existence may rest on what Kay knows. Too bad you wiped out his memory of it. Bring him in. Now. (..)2002 Men in Black II
(..) with your host, Peter Graves. Although no one has ever been able to prove their existence... ... a quasi-government agency, the Men in Black... ... supposedly carries out operations here on Earth... ... in order to k eep us safe from aliens (..)2002 Men in Black II