Is there a Biblical basis for the claim that human life begins at conception?
Yes, there is, but it is not in a verse which states, "Human life begins at conception."
It requires understanding of a Biblical principle, and then connecting the Biblical "dots" to learn the Bible's view on the issue.
So let's begin with the first "dot," which is the Biblical principle involved.
1)The NT teaches that Scripture is not the only source revealing the existence and nature of God, but that nature itself is also divine revelation.
". . .what may be known about God is plain to them (men who suppress the truth by their wickedness) because God has made it plain to them. For since the creation of the world God's invisible qualities--his eternal power and divine nature--have been clearly seen, being understood from what has been made, so that men are without excuse." (Rom 1:18-21)
The OT likewise teaches that God can be known in creation (Ps 19:1-4, 97:6).
Then the NT goes on to say that God's moral will is also known from nature. Speaking of the same group as Rom 1:18-31, it says that, "Although they know (from creation alone) God's righteous decree that those who do such things deserve death, they not only continue to do these very things but also approve of those who practice them." (Rom 1:32)
What the NT is referring to here is called natural divine revelation, as distinct from special divine revelation from God himself, in the Bible. It is called natural because it is revealed in nature,
and while it is outside the Bible, the NT presents it as authoritative (men are without excuse for not knowing about God from nature alone, and are morally responsible
for practices contrary to God's righteousness, revealed in nature alone).
Take a moment to let this Biblical principle sink in.
There is authoritative revelation outside the Bible--in creation. It is authoritative because by that revelation mankind is held accountable. Nature reveals the existence of God, it reveals his nature (eternal, divine, righteous). Likewise, the laws in God's nature reveal how his nature works; for example,
animal life cannot exist without food and water, rendering false any assertion that, under the right conditions, animal life can live without food and water;
"what goes up must come down," rendering false any assertion that some matter is not subject to the force of gravity;
plants begin as seeds, rendering false any assertion that we can feed the world without the use of seeds;
evaporation condenses into rain, rendering false any assertion that rain is exhaustive.
Granted, these examples limp, but you get the point: the laws in God's nature are authoritative regarding how his nature works, and it is at our own peril that we conjure up new laws by which to operate.
The upshot of this Biblical prinicple is that basing (by some very strange occurrence) an immoral act on one of these false assertions about nature, does not remove the immorality of the act,
because the laws in nature (authoritative natural revelation) reveal the basis of your claim justifying your immoral act to be false, therefore there will be accountability for that immoral act.
2) So having shown the Biblical principle regarding the authority of natural divine revelation as seen in creation (Rom 1:19-21), let us move to the second "dot,"
which is to examine what this Biblical principle (authoritative natural divine revelation in creation) reveals in regard to life in the womb.
Let's do this by the Socractic method, questions.
What kind of life is in a corn seed, corn life or cotton life? When the corn seed is planted in the ground, what kind of life begins to grow, corn life or cotton life?
And what kind of life is in a cotton seed? When the cotton seed is planted in the ground, what kind of life begins to grow?
And what kind of life is in human seed? When human seed is planted in the womb of a woman, what kind of life begins to grow?
Is there any time when the life produced by the corn or cotton seed is not corn or cotton life, but is tomato or grape life instead?
And because God's laws in his creation make clear the nature of seeds, neither is there any time when the life produced by human seed (Lev 15:16-18,32, 1 Pet 1:23) is not human life,
but generic "animal life" instead.
Note that when the corn plant, the tomato plant, the cotton plant and the grape plant sprout, they all look very much the same, and continue to do so through the initial stages of growth to the green shoot,
so that we can hardly tell them apart. Does that mean they are all the same kind of life, just generic "plant life," rather than corn, tomato, cotton and grape life, respectively? It does not.
Plants are never just generic "plant life" because of the nature of the seed. Generic life does not exist in God's nature, life is always a particular kind of life, determined by the nature of the seed (Lk 6:44).
Generic life is only an abstraction, whereby we classify similar groups of objects.
So God's natural divine revelation in creation (Rom 1:18-21) reveals that the nature of seeds does not allow for a simple generic form of life from a seed,
but that its life is a particular kind of life, determined by the nature of the seed, from the moment that it is life at all.
And so it is, that when we "connect the dots" between God's special divine revelation (the Bible), which reveals the prinicple of his authoritative revelation in nature (Rom 1: 19-21),
and which is where we find the nature of seeds,
God clearly reveals in nature that life in the womb from human seed (Lev 15:16-18,32, 1 Pet 1:23) is human life from the moment of conception.
And then finally, do we find this principle, which is revealed in the natural divine revelation of creation, reflected anywhere in the special divine revelation of the Bible? Yes, we do.
Exod 21:22-25 makes clear that prenatal and postnatal life are the same, for the penalty for killing the fruit of the womb is (human) life for (human) life in the womb (v.23).
Note the penalty for killing "animal life" (Lev 24:21) is not the same as the penalty for killing the fruit of the womb (Exod 21:23), because the fruit of the womb is not just generic animal life, it is human life and killing it requires the death penalty.
NB: The penalty for killing the pregnant woman is dealt with in Gen 9:6, Exod 21:12, Lev 24:17,19-21, Deut 19:11-13,21.
So the Biblical basis for human life beginning at conception should be clear, from both special divine revelation (Exod 21:22-25) and the nature of seeds, which is revealed in God's natural divine revelation in creation (Rom 1:19-21).