At the level of a Word-Study, no. Genus introduces a new and different idea.
בְּצַלְמֵ֖נוּ = bəṣalmênū
https://biblehub.com/hebrew/6754.htm Image, Likeness, Phantom
κατ᾽ εἰκόνα ἡμετέραν
https://biblehub.com/greek/1504.htm Image
כִּדְמוּתֵ֑נוּ = kiḏmūṯênū;
https://biblehub.com/hebrew/1823.htm - figure, form, likeness, resembling
καὶ καθ᾽ ὁμοίωσιν
https://biblehub.com/greek/3669.htm
Neither "image" nor "likeness" is perfect and the semblance to the original words is so loose they can virtually be swapped round without losing anything further.
God isn't described as having a beginning - and it's normal to understand him as the uncreated creator e.g. based on Psalm 90:2 "Before the mountains were brought forth, or ever you had formed the earth and the world, from everlasting to everlasting you are God.", Isaiah 43:10 - "Before me no god was formed, nor will there be one after me." Exodus 3:14 - "I AM WHO I AM." Genesis 1:1 - "In the beginning God created"
And that takes him out of the most important part of the word genus' register.
It's possible there might be some specific senses of genus that fill in gaps in our words image or likeness. But it's for Nepesh Roi or the OP to explain that.
- Clearly it's not image to the exclusion of real qualities. At Genesis 3:22 there is acknowledged real similarity between Adam and God
Then the Lord God said, “Behold, the man has become like one of us in knowing good and evil. Now, lest he reach out his hand and take also of the tree of life and eat, and live forever—”
Our relationship to God is that of children to a Father. If anything, our earthly relationships are provided to us to help us understand God's love.
The breath of God animates Adam, so part of us is categorically alike to the Father
But those things don't imply there is a genetic likeness (in the non-scientific sense of genetic) between man and God. If the similarity is taken to an extreme and the events of Genesis are not Adam's creation so much as his demarcation from the rest of God, and Eve knew the difference between good and evil anyway, and they don't really die - then genus still becomes the improper word, because Adam's entry to the world is the world's genesis, and he no longer has one!
Genus is potentially quite dangerous - because it not only introduces a new term, but a floating one with an even wider register than what it's standing for. It's surely safer to read 'likeness' or 'image' whilst remembering that translation isn't 1:1, and that the fact Genesis 1:26 is translated "Let us make man in our image, after our likeness" doesn't give us a general right to draw converses like "God is visible." or "God has two arms and two legs."