God is fine with eating meat.
For instance, look at the story of Cain and AbleAbel:
Next she bore his brother Abel. Now Abel was a keeper of sheep, and Cain a tiller of the ground. In the course of time Cain brought to the Lord an offering of the fruit of the ground, and Abel for his part brought of the firstlings of his flock, their fat portions. And the Lord had regard for Abel and his offering, but for Cain and his offering he had no regard. So Cain was very angry, and his countenance fell.
Genesis 4:2-5
Now, Christian denominations debate exactly why God rejected Cain's offering of plants and accepted Abel's offering of meat - some argue that God has a preference for meat over plants, some that Cain offered some random portion of his harvest while AbleAbel offered the very best parts of his, or that AbleAbel was making a proportionally larger sacrifice - but regardless of the specific reasons, it's clear that God is okay with the consumption of meat.
Additionally, later on in the Bible, we can see God repeatedly demanding animal sacrifice being conducted for Him, ultimately culminating in the sacrifice of Jesus Christ for humanity's sins. It certainly appears that God has no issue with animals suffering for human gain.
However, humanity is called out to be good husbands over the animals of the Earth that we have been given dominion over, so we should avoid pointless or greedy cruelty; for instance, the Law of Moses commanded that oxen were to be allowed to eat a portion of the grain they helped harvest while they worked.