1. Hold that the personal pronouns up to John 1:11 or 1:14 refer to the Logos but not Jesus.
In the particular line you are quoting, John 1:10, the pronouns can be understood to refer to the Logos. It can be translated as
"The Logos was in the world, and the world came into being through the Logos, and
the world did not know the Logos."
Logos is a masculine noun, and so fits the pronouns here. If you think the Logos is not = to Jesus, then this line isn't stating Jesus pre-existed.
Indeed, this is basically how the Revised English Version translates this line, where they use 'it' instead of 'he' or 'him'. In commentary on John 1:10 they say
"John 1:10 shows that the logos, God’s express purpose and plan was in
the world, and it also repeats in a different way what had been stated
in John 1:3, that it was through the logos that God made the world.
However, John 1:10 adds that the world did not know the logos and thus
by implication the world did not know God."
It is possible to hold that the masculine pronouns are referring to the Logos right up to John 1:14's introduction of the 'only begotten'.
In the case of the Revised English Version commentary, they hold that John 1:1-10 is "a kind of inclusio," and then at John 1:11 John switches from the Logos to 'the Logos made flesh'.
2. Hold that the pronouns referred to above may or may not refer to Jesus, but also hold that the 'beginning' which is being talked about in John 1 isn't the beginning of Genesis, but the beginning of Jesus' ministry and the 'new creation'.
You see this with the Racovian catechism (p. 63).
"As then the matter of which John is treating is the Gospel, or the
things transacted under the Gospel, nothing else ought to be
understood here besides the beginning of the Gospel; a matter
clearly known to the Christians whom he addressed, namely, the advent
and preaching of John the Baptist, according to the testimony of all
the evangelists, each of whom begins his history with the coming and
preaching of the Baptist. Mark indeed (chap. i. 1,) expressly states
that this was the beginning."
Compare John 15:27 ("you have been with Me from the beginning.") or John 16:4 ("from the beginning"). So what is being described at John 1:11 according to this is the new creation which has come into being.
3. Hold that John 1:1-5 refers to God's word, Jesus is referred to first at John 1:7, and is the referent straight through to John 1:18. This is the approach Anthony Buzzard takes in The One God, the Father, One Man Messiah Translation: New Testament with Commentary.
"1 In the beginning was the word, and the word was with God, and the
word was fully expressive of God Himself. 2 This was with God in the
beginning. 3 Everything came into existence through it, and without it
nothing of what came into being existed. 4 In it there was life and
that life was the light of men. 5 And the light shines in the darkness
and the darkness does not overwhelm it.
6 There came on the scene of history a man sent from God. His name was
John. 7 This man came as a witness so that he might bear witness to
the Light and that everyone might believe through him. 8 He was not
the Light himself, but he witnessed concerning the Light.
9 This was the genuine Light which enlightens every man coming into
the world. 10 He was in the world and the world came into existence
through him, and the world did not recognize him, the Light. 11 He
came to his own land and his own people did not accept him. 12 As
many, however, as did accept him, to these he gave the right to become
children of God — namely the ones believing in his Gospel revelation.
13 These were born not from blood, nor from the desire of the flesh,
nor from the desire of a male, but from God.
14 And the word came into existence, a human being, and tabernacled
among us, and we beheld his glory, the glory such as a uniquely
begotten Son enjoys from his Father, full of grace and truth. 15 John
gave his witness concerning him and cried out with these words, "This
was the one of whom I said, 'The one coming after me has now moved
ahead of me, because he always was my superior.'" 16 For from his
fullness all of us have received grace and more grace. 17 For the Law
was given through Moses, but grace and truth came through Jesus
Messiah. 18 No one has seen God at any time. A uniquely begotten Son,
one who is in the bosom of the Father — he has explained God."
I have preserved the paragraph formatting from Buzzard's translation, as it helps highlight the flow of ideas.
Note the lower-case 'light' until John 1:7, which indicates the shift to a reference to Jesus (the logos made flesh). A key here is that the 'beginning' of John 1:1 on a straightforward reading refers to Genesis' beginning, but John 1:10 which seems largely a repetition is rather a development of John 1:3, applying the idea to the 'new beginning' which is the ministry of Jesus. So the 'world came into existence' at John 1:10 is referring to the new creation brought about through Jesus, not the original creation in Genesis.
Buzzard's translation is the first of John 1 (whether trinitarian or unitarian) I have read to make sense to me, as a whole and in terms of how it develops the narrative through John 1.