I carefully read Hebrews 11:6

And without faith it is impossible to please him, for whoever would draw near to God must believe that he exists and that he rewards those who seek him.

Read that middle part:

for whoever would draw near to God must believe that he exists...

Doesn't that seem obvious?  Yet, that's exactly what it says.

"...He exists..." - ἐστί - third person singular, "to be" - He IS.

And yet...(even as I write this the connection hits me)

First person singular:  I AM.  And the Old Testament statement that comes to mind...

God said to Moses, "I AM WHO I AM." And he said, "Say this to the people of Israel, 'I AM has sent me to you.'" (Exo. 3:14)

"I AM" -  הָיָה (hayah) - "to be".

It's such an odd statement - in order to get close to somebody you seek, you must believe that it exists.  Well...um...yes.

But if you but the "HE IS" alongside the Old Testament "I AM" , is it possible that the Hebrews passage is telling us that if we want to draw near to God, we must first come to the conviction that we stand before the "GREAT I AM", justified by grace, through faith.

Not the fluffy "feel good", "love is never having to be told I'm wrong" Jesus that we find too often in today's "theology lite".

No...the I AM who spoke creation into existence, the Father who gave His Son, the Son who died and the Spirit who convicts us of sin draws us.

In order to get close to God"...we have to believe in "I AM".