Jesus said, “the one who sees Me sees Him who sent Me” (Jn 12:45 NASB). Jesus is not the image of God in any visible or physical sense, for God is Spirit (Jn 4:24). In addition to the answers already given, another way to approach the OP’s question is from the perspective of the gospel of John, which details the ways in which Jesus makes the Father “visible".

Everything that Jesus does reflects the work of the Father.

Therefore Jesus answered and was saying to them, “Truly, truly, I say to you, the Son can do nothing of Himself, unless it is something He sees the Father doing; for whatever the Father does, these things the Son also does in the same way. – Jn 5:19

The words that Jesus speaks are the words of the Father. However, the words are part of the work, and thus the two are not distinct from each other but are separated only for the sake of discussion.

I do nothing on My own, but I say these things as the Father instructed Me. – Jn 8:28

And I know that His commandment is eternal life; therefore the things I speak, I speak just as the Father has told Me. – John 12:50

And the word which you hear is not Mine, but the Father’s who sent Me. – Jn 14:24

Though no one has seen the Father, Jesus makes him known (Jn 1:18; cf 1 Jn 5:30, 1 Cor 2:16). Ultimately, everything that Jesus says and does serves to reflect and reveal the Father.

The one who has seen Me has seen the Father; how can you say, ‘Show us the Father’? 10 Do you not believe that I am in the Father, and the Father is in Me? The words that I say to you I do not speak on My own, but the Father, as He remains in Me, does His works. – John 14:9-10

Per the OP's reference to 1 Pet 2:24, even Jesus' dying for our sins is a demonstration of the Father’s love.

But God demonstrates His own love toward us, in that while we were still sinners, Christ died for us. – Rom 5:8

The word image in Col 1:15 does not refer to a picture or a cutout of paper or other material. Consider how, when we say a son is the “spitting image” of his father, we do not mean that the son is not a real person in his own right. Likewise, Jesus is at once always a real person and always the image of God. These two aspects are not mutually exclusive.

Jesus said, “the one who sees Me sees Him who sent Me” (Jn 12:45). Jesus is not the image of God in a visible or physical sense, for God is Spirit (Jn 4:24). Jesus makes Him visible in the sense that he makes God known and understood. One way to approach the OP’s question is from the perspective of the gospel of John, which details the way in which Jesus makes the Father “visible.”

No one has seen God at any time; God the only Son, who is in the arms of the Father, He has explained Him. – Jn 1:18

Jesus came to fulfill the Father’s will.

For I have come down from heaven, not to do My own will, but the will of Him who sent Me. – Jn 6:38

Everything that Jesus says and does reveals the words and works of the Father.

The words that I say to you I do not speak on My own, but the Father, as He remains in Me, does His works. – John 14:10

Even Jesus dying for our sins (1 Pet 2:24) is to demonstrate the Father’s love. Though no one has seen God, Jesus makes Him known: His will, His works, and ultimately, His love.

But God demonstrates His own love toward us, in that while we were still sinners, Christ died for us. – Rom 5:8