Conventional translation: Without faith, it is impossible to please God, because everyone who comes to Him must believe that He is (exists), and is a rewarder of those who diligently seek Him.

Literal Greek to English: Apart from faith it is not possible to be well-pleasing to God since it is necessary for all who approach Him to believe that He is and becomes/turns out being rewarder of those earnestly seeking Him.

Hebrews was written for believers in God, so dispelling atheism doesn’t seem to be a factor. Thus, NIV use of ‘exists’ can safely be bettered. The issue seems rather that often believers don’t put what faith they have in enough of God (quality), or enough of faith in the God of prayer/worship/spiritual relations (quantity).

Optimal rendering: Being well-pleasing to God cannot happen/is not possible without faith since everyone who comes near/approaches Him must believe that He is (really God, is Who He is, Who is right there, He Is I Am) and as such/namely: ends up being/turns out to become Rewarder of those sincerely seeking Him.

The point of the Christian life of faith is to trust God as God -nothing less- and to full-on commit to this full-on God 100% as He enables the mustard seed to full-bloom. Believe what you can and trust the Lord for what you can’t so that relational trust overcomes doubting unbelief in any supremely challenging situation or normal need requiring miraculous or ordinary provision.