Why Incarnation from Spirit is possible
In Christianity understood through the Nicene creed, "God" in John 4:24 is God the Father, so it is correct to say that God the Father is spirit. In Christianity, God created everything, including all human beings who have a body as well as a soul made "in God's image". Incarnation (God taking a human nature) is possible simply because this is the God who made human beings in the first place. Therefore, God could also assume the form of a perfect human being (lesser than God), although in order to do that He would need to shed some of His divinity (Phil 27:7).
How God became human and stayed with us in spirit
According to Nicene theology, God was conceived miraculously in a hypostatic union of God and human within the womb of Virgin Mary, who then gave birth around 3-4 BC in Bethlehem. The kind of this union was determined to be fully God and fully human at the same time, formalized at the Council of Chalcedon.
After Jesus's ascension, his whole glorified & resurrected body left our universe but as a replacement Jesus sent His divine spirit to live with us (starting at Pentecost), whom Christians call the Holy Spirit.
Because the spirit of Jesus is 100% God, Christians can also worship Jesus as God without committing blasphemy (since Jesus is not simply a created being like humans or angels). For the meaning of worshiping "in spirit and truth", see this gotquestion.org article What does it mean to worship the Lord in spirit and truth?.
Why God incarnated into Jesus
Why did God do this, though? He did this mainly to save humanity, but there are other purposes as well such as:
- to reveal the Father to us
- to fulfill the Davidic covenant, and
- to provide an example for our lives on how we ought to live.
See Charles Ryrie's The Purpose of the Incarnation and Rev. Campbell Morgan's article.
For further study
The doctrine of God's taking human form is called Incarnation
For more understanding on why incarnation is necessary for salvation according to Nicene theology, one historically significant doctrine is Recapitulation developed by an early church father Irenaeus (125-202 AD). You can read more about Recapitulation by reading this 2015 paper Irenaeus of Lyons: A Defense of Recapitulation).