If death entered the world through man’s sin (Rom 5:12), how could the first people kill animals to eat?

Romans 5:12
12 Wherefore, as by one man sin entered into the world, and death by sin; and so death passed upon all men, for that all have sinned:
KJV

The sixth day creation were not farmers, they were given dominion over all living creatures and herb bearing seed. The people of the land of Nod (Nod means wandering,) were nomadic people, not farmers.

People only started farming when Adam and Eve were created:

Genesis 2:5
5 And every plant of the field before it was in the earth, and every herb of the field before it grew: for the LORD God had not caused it to rain upon the earth, and there was not a man to till the ground.
KJV

About Death:

“Death” is another name of Satan, when Adam and Eve sinned, they sold out dominion of the world to Satan.

Hebrews 2:14
14 Forasmuch then as the children are partakers of flesh and blood, he also himself likewise took part of the same; that through death he might destroy him that had the power of death, that is, the devil;
KJV

Revelation 6:8
8 And I looked, and behold a pale horse: and his name that sat on him was Death, and Hell followed with him. And power was given unto them over the fourth part of the earth, to kill with sword, and with hunger, and with death, and with the beasts of the earth.
KJV

NT:622
apollumi (ap-ol'-loo-mee); from NT:575 and the base of NT:3639; to destroy fully (reflexively, to perish, or lose), literally or figuratively:

KJV - destroy, die, lose, mar, perish.

NT:684
apoleia (ap-o'-li-a); from a presumed derivative of NT:622; ruin or loss (physical, spiritual or eternal):

KJV - damnable (-nation), destruction, die, perdition, perish, pernicious ways, waste.