Did God's essence enter time and space?

Clarifying the question

Short answer is: Yes, but "entering creation" needs a more precise definition.

Also, your question as it's presently worded (Oct 31, 2021) lacks scope. I'm going to answer from the perspective of Trinitarian Christians, who most subscribe to the Nicene Creed which says (emphasis mine)

We believe .... in one Lord Jesus Christ, the Son of God, ... of the essence of the Father ..., begotten, not made, consubstantial with the Father; ... Who for us men and for our salvation came down and was incarnate and was made man; ...

and to the Chalcedonian Creed, which clarifies the nature of the incarnation (emphasis mine):

We ... teach people to confess one and the same Son, our Lord Jesus Christ, the same perfect in Godhead and also perfect in manhood; truly God and truly man, of a reasonable [rational] soul and body; consubstantial [co-essential] with the Father according to the Godhead, and consubstantial with us according to the Manhood; in all things like unto us, without sin; begotten before all ages of the Father according to the Godhead ...

This answer interprets your question as follows:

• "God's essence" to mean God the Son who is "of the essence of the Father" and "consubstantial with the Father" (cf. Nicene creed)
• "enter creation" to mean "came down" and "was incarnate and was made made man" (cf. Nicene creed)

How does God's essence "enter creation"

Trinitarian Christians believe that the creator God's essence was involved somehow within His creation through Incarnation by one of its hypostases (persons) "adding on" a fully distinct human nature at the time of the Holy Spirit's overshadowing the Virgin Mary at conception. After probably the normal 9 month gestation period Jesus was born naturally as baby Jesus, usually pictured at Christmas time placed in the manger. After birth, Jesus then grew "in wisdom and stature" until reaching adulthood (Luke 2:52).

Throughout Jesus's life on earth he retains both his dual human and divine natures "unconfusedly, unchangeably, indivisbly, inseparably", according to the Chalcedonian Definition. Eleonore Stump in an interview video Jesus as God explains in everyday language how this Incarnation works, likening this to an actor with perfect vision who needs to take on a role of a blind man. He does this by wearing a very dark contact lens. Therefore, the actor does not lose his perfect vision, and has the option to remove the contact lens when he needs to access his perfect vision.

For a more technical description, you can read the article Did God's Essence Become Incarnate?

We have to say that God’s essence did not change into something else at the Incarnation. At the same time, we have to say that God’s essence was involved in the Incarnation. The Reformed scholastics help us out here. Their formulation is that God’s essence is incarnated, but only in one of its hypostases or persons (see Richard Muller, Post-Reformation Reformed Dogmatics, volume 4, p. 211). The process of incarnation is one of addition. A full human nature is added, taken up in hypostatic union with the second person of the Trinity, the essence of God in the second person. This must not be understood in any way that would imply that a separate already-formed human person was joined to the divine person. The full human nature (body and soul) of Christ only ever exists in hypostatic union with the divine nature. This being said, the Father and the Holy Spirit were not passive spectators in the Incarnation either. All the outside works of the Triune God are indivisible (which means that all three persons of the Trinity are at work in everything God does). The Father sent both the Son and the Spirit in the process of incarnation, and the Holy Spirit overshadowed Mary. This must qualify what was said about only the second person being incarnated. For while it is true that only the second person became incarnated, yet it is also true that the Father and the Holy Spirit were involved.