The verb that is translated "is close to" here is used 947 times in the OT, and is "know/known" 750 of those times. It is never translated with a word related to "close" or "proximate" in the KJV (which is the version that my software uses).
Psalm 34:18 is a better source for the concept of God's nearness in the OT:
The LORD is near the brokenhearted; he saves those crushed in spirit.
In the New Testament, I would look to Acts 17:27-28
... he is not far from each one of us. For in him we live and move and have our being.
I'll let you be my spokesperson.
My job is more mental anyway.
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