How do Christians who are neither Evolutionists nor Young Earth Creationists explain the timeline of the six days of creation in Genesis chapter 1?

Your question suggests that “no time-line is required” in order to believe and understand the six days of creation, and that “the time factor would not be the point”. As a Christian who denounces evolution and who believes that God is the creator of time, space, matter and all life, allow me to quote from a booklet written by mathematician and Christian, John Blanchard.

“The analytical philosopher Ludwig Wittgenstein said, “The riddle of life in space and time lies outside space and time.” Modern science tells us that the universe has at least five essential elements – time, intelligence, energy, space and matter – and all are to be found in the Bible’s opening sentence: ‘In the beginning, God created the heavens and the earth.”

In the beginning’ speaks of time, ‘God’ speaks of intelligence, ‘created’ speaks of energy, ‘the heavens’ speaks of space, and ‘the earth’ speaks of matter.

Oxford Don Keith Ward says, “To grasp an idea of God is to grasp an idea of the only reality that could form a completely adequate explanation of the existence of the universe.” (Source: Booklet entitled ‘Is There Anybody Out There?’ E.P. 2006, pages 16 to 17)

Nowhere in the book of Genesis does it say anything about when “the beginning” started. Indeed, as God has existed without any starting point in time as we know it that is hardly surprising.

One problem is that people keep mixing up the theory for the origin of the universe with the theory of evolution. This is because vast aeons of time are required for both theories to 'work'. However, if the biblical 'days' of creation are not limited to 24-hour earth hours, and if each 'day' of creation can be taken as an unknown period of time, then the time-line from the start of our universe till the creation of Adam and Eve by God is no longer an issue.

The Bible tells us that God spoke the universe into being, creating out of what cannot be seen. Science knows that prior to the existence of time there was a singularity - which is science-speak for admitting that the laws of physics we work with couldn't apply as some physical things like temperature or density become infinite in value. As a Christian I believe that it was God who created energy (the atom), time, space, matter and light and how He did it and how long it took is not the point. Science also knows that universal light had to arise before any life could form, and that fits in with God creating light on day one. After God created light, then the biblical phrase of "there was evening then there was morning," begins to make scientific sense.

This means that the simple answer to your question is that there’s no need to ‘explain’ the time-line if the term ‘days’ has various meanings in Genesis, and the rest of the Bible (see footnote). There’s only a need to explain its order of events if the days are literal 24-hour-earth-days. Finally, a word on the balance that is needed between Christianity and science:

“The challenge for Christianity is to take science seriously. Science, of course, doesn’t answer every question… It grieves me when I see people – who I’m sure are sincerely wishing to serve the God of truth – refusing to see the truth in science. That is a sad and ultimately unhelpful situation. People of faith need to be grateful for science and welcome truth.” (Interview with Rev. Dr. John Polkinghorne fellow of the Royal Society, former Professor of Mathematical Physics at Cambridge University, as published in ‘War Cry’ issue 14 January 2012, pp 8 to 11)

Footnote: The Hebrew word ‘yom’ which translates into English as ‘day’ has many different meanings: NASB Translation: afternoon* (1), age (8), age* (1), all (1), always* (14), amount* (2), battle (1), birthday* (1), Chronicles* (38), completely* (1), continually* (14), course* (1), daily (22), daily the days (1), day (1115), day of the days (1), day that the period (1), day's (6), day's every day (1), daylight* (1), days (635), days on the day (1), days to day (1), days you shall daily (1), days ago (1), days' (11), each (1), each day (4), entire (2), eternity (1), evening* (1), ever in your life* (1), every day (2), fate (1), first (5), forever* (11), forevermore* (1), full (5), full year (1), future* (1), holiday* (3), later* (2), length (1), life (12), life* (1), lifetime (2), lifetime* (1), live (1), long (2), long as i live (1), long* (11), midday* (1), now (5), older* (1), once (2), period (3), perpetually* (2), present (1), recently (1), reigns (1), ripe* (1), short-lived* (1), so long* (1), some time (1), survived* (2), time (45), time* (1), times* (2), today (172), today* (1), usual (1), very old* (1), when (10), when the days (1), whenever (1), while (3), whole (2), year (10), yearly (5), years (13), yesterday* (1). http://biblehub.com/hebrew/3117.htm