Probably various people have held every possible shade of opinion on this issue. The idea that heaven is not a true "place" in the material world (in the sense that Earth is a place) is much, much older than the Big Bang theory. Remember that Christians have had the book of Genesis - which asserts that God created everything at some definite time in the past - for much longer than they've known about the Big Bang.
A common line of interpretation sees Genesis 1:1 as describing how God is the author all things visible and invisible. In this view, the heaven of verse 1 is not a place in the universe, but stands for spiritual things in contrast to material things. Augustine (City of God 11.33-34) thinks this the most probable reading, though he stresses that we shouldn't think that there's anything inherently "wrong" with matter - this is in opposition to the Manichean idea that the world is a kind of prison for souls.
One problem with this reading is that the rest of Genesis 1 seems to say that the same "heaven" is where birds fly (v20 uses the same Hebrew word). But as Thomas Aquinas observes (Summa Theologica 1.68.4), the word "heaven" is used in many senses elsewhere in Scripture. This is a common linguistic phenomenon even today, as for example le ciel in French may mean "heaven" or "sky", or even "space". So we find that "heaven" may mean the airy place where you find birds and clouds, or the place where stars and planets are (further subdivided by planetary orbits, etc.), or the state of being united with God. Notice that this last one is not described as a place, though by analogy we may think and speak of it as being a place. We speak of it as being "above" us, and associate it with the celestial bodies: which give light, are made by God, and are beyond our everyday commonplace experience. Sometimes this is done deliberately, for poetic effect.
Compare Basil the Great in Homilies on the Hexaemeron, who distinguishes between heaven (Genesis 1:1), the firmament (the starry vault, v6) and the atmosphere (v20), saying that the firmament and atmosphere are called "heaven" only by analogy with the true heaven. He dismisses all attempts at discovering what substances heaven might be made from - which was a common philosophical question. In the same way, John of Damascus (Exact Exposition of the Orthodox Faith 2.6) declares that the essence of heaven is beyond our knowledge.
These and other authorities did try to "locate" heaven with respect to the Earth, using the best astronomy of the day. They believed that beyond the "sphere of the fixed stars", there was a final boundary sphere, the firmament, beyond which was the endless expanse of the "empyrean heaven". (And again, any part of this, from the atmosphere upwards, could commonly be called "heaven", as John of Damascus admits.) Once in the empyrean, however, there's no longer any notion of time or space. This comports with Aristotelian philosophy, which was tremendously influential. Boethius (in Quomodo substantiae) observes that the proposition "Incorporeal things are not in any place" is one which may make sense only to the educated - the full-blown concept of the timeless, spaceless, incomprehensible empyrean is a tricky one, and so it's easy to fall into a more naive conception of heaven as simply a faraway place. The point of the empyrean is not that it's "a place" beyond the stars, but that it's outside the ordinary material universe, of which the firmament was thought to be the boundary.