You should enable exceptions and instantiate in a try-catch block.
It is not obvious from the documentation but if you use the constructor to open the database it will throw an exception on error.
Further if you set the flag SQLITE3_OPEN_READWRITE in the second argument then it will also throw an exception when the database does not exist (rather than creating it).
class Database extends SQLite3
{
function __construct($dbName)
{
$this->enableExceptions(true);
try
{
parent::__construct($dbName, SQLITE3_OPEN_READWRITE );
}
catch(Exception $ex) { die( $ex->getMessage() ); }
}