Edit: while I still believe the trajectory discussed below is valuable, and appreciate the votes, I believe the other info in this answer is important: https://hermeneutics.stackexchange.com/a/66370/43095
where Perry Webb outlines based on the Greek that, “Basically, Logos/Word in the New Testament does not always mean Jesus as it does in John 1:1-18. The same can be said for light. It does not always mean Jesus, even in John 1.” And a case can be made for the Logos first entering as Christ in 1:9. Importantly, it cannot be viewed as a different Logos though, as proven below.
“We are told in v14 that the logos became flesh. This refers to Jesus and his subsequent conception and birth through Mary. This question seeks to determine if it can be shown biblically that Jesus is not that logos referred to in John 1:1-3 and is the logos only at a later time based on v14?”
It cannot be shown biblically, and I personally do not know of any groups that claim this. While I can understand the OP’s reading of it and the enquiry, a closer examination uncovers the implausibility. If this was at all debatable after a careful read, then I would seek outside confirmation and citation, but we can probably agree. The reason that it cannot be shown biblically is the ongoing bridge from 1 through 14, including at a couple key spots. 1 through 14 quoted below and inline a bit (all NIV)
First to motivate the question, notice that the early verses of John are discussing the time of “the beginning”, then by 3 it’s already up to creation, and 4 says that man is being made in God’s image and it is being emphasized (some may think it is being ‘learned’) that this required the light of the Logos to do so. Exact agreement on that summary of 4 is not needed. Then 5 is in the present tense. But by 14 Logos is being made flesh. Is that only part of the original Logos, the same Logos at all, or a different one, or a combination, or what?
We can make the bridge obvious going forward from 3 and backward from 14. Ultimately the bridge is 6 and 7, John the Baptist. But 9 is the clincher. Via 9, not 14, the question is answered. Jesus is in 10 and The Logos as the Light in 8. Then 9 is the light, the whole light*, and only the light, coming into the world:
9The true light that gives light to everyone was coming into the world. (all NIV)
The challenge was that this fact was not listed in 14, and we had to find it. So it wasn’t immediately clear if it was only the Logos, and/or if it was all of the Logos. The rest of this answer is just the details of bringing Jesus Christ backwards to 10 and the Logos forward to 8, but that’s probably close to obvious by a mere reading of it now that it has been emphasized explicitly.
Even by the OP, 14 is Jesus Christ. Reading 12 and 13 as a unit, 12 is clearly about Jesus Christ Himself and 13 is being born again.
12Yet to all who did receive him, to those who believed in his name, he gave the right to become children of God
10 by itself might be less than completely obvious (or at least disputable) that it is Jesus, but when combined with 11:
11He came to that which was his own, but his own did not receive him.
10He was in the world, and though the world was made through him, the world did not recognize him.
Now trace from 3 to 8. From here just see the main quote, emphasis mine. 3 is clearly the Logos with God, in creation. The almost parallel construction beginning 3 and 4 makes it therefore clear that 4 is as well. “3 Through him all things were made.. 4 In him was life..” Obviously same “him”. Being the same as “him” in 3, “The light” subsequently carries on unchanged from 4 through 8. It probably seems like a no-brainer after all that, but I had the same question.
In Summary: It cannot be shown Biblically from those verses that a different Logos is being discussed.
1In the beginning was the Word, and the Word was with God, and the Word was God. 2He was with God in the beginning. 3Through him all things were made; without him nothing was made that has been made. 4In him was life, and that life was the light of all mankind. 5The light shines in the darkness, and the darkness has not overcome it.
6There was a man sent from God whose name was John [the Baptist]. 7He came as a witness to testify concerning that light, so that through him all might believe. 8He himself was not the light; he came only as a witness to the light.
9The true light that gives light to everyone was coming into the world. [now and hereafter in the world] 10He was in the world, and though the world was made through him, the world did not recognize him. 11He came to that which was his own, but his own did not receive him. 12Yet to all who did receive him, to those who believed in his name, he gave the right to become children of God - 13children born not of natural descent, nor of human decision or a husband’s will, but born of God.
14The Word became flesh and made his dwelling among us. We have seen his glory, the glory of the one and only Son, who came from the Father, full of grace and truth.
*“whole” is not entirely correct, but how to settle that specifically is debatable, and debated. And beyond this question anyway.