According to Protestant theology, does God’s omnipresence entail us humans walking into God all the time?

God's point of view

God is Spirit, so we don't "collide" into God physically. Moreover, God's "primary residence" is in Heaven, which is outside space and time of our universe. But He upholds all creation, aware of everything that is happening within creation, and can speak to our conscience too. So in that sense he is omnipresent within creation.

Psalm 139 describes God's intimate knowledge of the excruciating details of our lives, not just physically, but in our mind as well. For the wicked, this should be scary, but for believers it's a beautiful assurance that wherever we are, God is there, even in our future, even in our thoughts. We don't need to go to a temple to pray, God is accessible everywhere. This assurance of God's mode of knowing us is repeated and implied in several places of the Bible, including Jesus's saying in Matt 10:30 ("even the very hairs of your head are all numbered").

Human point of view

But that's from God's point of view. From human point of view, it's not like we can "find" him even though we look for him IF He doesn't want his presence known. But traces of Him can be found in the beautiful nature, the fecundity of the animals and plants, etc. This, coupled with being a witness in our conscience, is what Paul meant in his letter to the Romans that no one is without excuse for saying that God does not exist (Rom 1:19-20).

God's knowing us intimately does NOT mean we are aware of Him. God, by his character, does not force himself to us. We are told to invite Him to our heart, and once we do, God will make his presence known. That's how God preserves our free will: ready to come in but don't intrude if we choose to reject Him.

These points are gleaned from a Reformed Protestant text-book on theology. First, how to understand this matter of "omni"... [whatever].

"Only God is independent, immutable, immortal, and eternal. This cannot be said of any creature. That is why most of these attributes carry the negative prefix and we call them incommunicable attributes - attributes that are not shared with us, even analogically. However, because human beings are created in God's image, they do share other attributes with God, analogically. Where we have attributes similar (analogous) to God's, he is always qualitatively different and greater. Therefore, these communicable attributes will often have the "omni" (all) prefix attached to them.

Wisdom, knowledge, and power are predicated of human beings, yet God is all-wise, omniscient, and sovereign. Our knowledge is always piece-meal and partial. We learn this, now that; we never comprehend every piece perfectly, much less the whole puzzle. God's knowledge is different. First, he does not learn anything because his knowledge is eternally perfect and comprehensive {Psalm 139:1-6 is cited along with other scriptures} God does not depend o the world for his knowledge any more than for his existence. No more than his omnipresence can his omniscience be limited or circumscribed within boundaries." (Pilgrim Theology, pp82-84, Michael Horton, Zondervan 2011)

This means that believers can only recognise (as did king David) that God is omnipresent, while we are not. We cannot explain nor understand it. We only come to realise it by God communicating something of that to believers, otherwise we wouldn't have a clue.

Further on, the author points out that what David said in Ps.139:7-10 also shows the omnipresence of the Spirit of God (p.93). I would add that the Son of God also shows his omnipresence (e.g. in Matthew 18:20 & John 20:24-27).

Of course, we can never be omnipresent, so this is an incommunicable attribute of Deity. We cannot even begin to understand it, yet when believers are born of the Spirit and have faith of Jesus Christ, their whole perception changes, for the better. There is nothing to fear, that God is everywhere present. It is awesomely wonderful and comforting. There is no idea of "colliding into God constantly", as you put it. Conversely, there is the sense of God being with us constantly. That is what David wrote about; that even if he wanted to flee from God's presence, he couldn't. He may well have wanted to flee for the year after his sin regarding Bathsheba - until he then repented of it, and knew restoration - but by the time he wrote Psalm 139 he was glorying in the wonder of God's omnipresence. He couldn't explain it, and neither can any of us. But whenever we sense God's presence, that brings us to worship.

εν αυτω γαρ ζωμεν και κινουμεθα και εσμεν [Acts 17:28 TR]

In Him, we live and move and have being [KJV, Acts 17:28]

'All things were made by him and without him was not anything made that was made' writes John at the beginning of his gospel account, speaking of Him who is called 'Logos' : 'and God was the Logos'.

Thus Paul makes clear to the Athenians that we live and move and are, in God.

This is clearly a spiritual presence for God, the eternal, who is from the beginning, is he who made all that is, other than himself.

And 'God is Spirit', saith Jesus.

One may not be aware of the Holiness and the Spirituality of God's presence within one's own spirit, and, if so, that is a matter of the necessity of being born again : of water and of Spirit, that we may know Him in whom we exist.

'Ye must be born again' said Jesus, expressing the necessity of a spiritual life in union with God himself that we might truly know him.