If God made Adam and Eve from mud and soil, from what matter did he create the other animals and living beings?
Any answer to this question will be supposition or guesswork, there are no biblical references that address what God used to create all the other creatures of the planet, only that He created them.
The only biblical support for the way God created life, outside of man, is with His words. Gods words have life in them as He alone has aseity.
Genesis 1: 20–28
20 And God said, Let the waters bring forth abundantly the moving creature that hath life, and fowl that may fly above the earth in the open firmament of heaven.
21 And God created great whales, and every living creature that moveth, which the waters brought forth abundantly, after their kind, and every winged fowl after his kind: and God saw that it was good.
22 And God blessed them, saying, Be fruitful, and multiply, and fill the waters in the seas, and let fowl multiply in the earth.
23 And the evening and the morning were the fifth day.
24 And God said, Let the earth bring forth the living creature after his kind, cattle, and creeping thing, and beast of the earth after his kind: and it was so.
25 And God made the beast of the earth after his kind, and cattle after their kind, and every thing that creepeth upon the earth after his kind: and God saw that it was good.
26 And God said, Let us make man in our image, after our likeness: and let them have dominion over the fish of the sea, and over the fowl of the air, and over the cattle, and over all the earth, and over every creeping thing that creepeth upon the earth.
27 So God created man in his own image, in the image of God created he him; male and female created he them.
28 And God blessed them, and God said unto them, Be fruitful, and multiply, and replenish the earth, and subdue it: and have dominion over the fish of the sea, and over the fowl of the air, and over every living thing that moveth upon the earth.
Genesis 2:7 - The only place that describes what God used in creation beyond His words.
7 And the Lord God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul.