Can you enter heaven if you do not know God?
Know God as in being in right relationship with Him, or know ABOUT Him?
God does not depend upon your efforts to keep you in His family. You get born from above and you are in His family. That's why He, GOD, took a human form to accomplish.
So when folks start believing it is up to them to get there and up to them to keep it in tact, well they insult the very Creation by God, for believing in Christ Jesus as Savior and Lord then gives HIM all the glory.
But men and women have this little pride thing which makes them want to take some of the credit for what God Alone can do. If you could be worthy of Salvation then Christ died for nothing. You will never be worthy of what God does on your behalf, to His Glory.