The NET Bible notes are helpful here:
tn The Hebrew term תְּהוֹם (tÿhom, “deep”) refers to the watery deep, the salty ocean – especially the primeval ocean that surrounds and underlies the earth (see Gen 7:11).
sn The watery deep. In the Babylonian account of creation Marduk killed the goddess Tiamat (the salty sea) and used her carcass to create heaven and earth. The form of the Hebrew word for “deep” is distinct enough from the name “Tiamat” to deny direct borrowing; however, it is possible that there is a polemical stress here. Ancient Israel does not see the ocean as a powerful deity to be destroyed in creation, only a force of nature that can be controlled by God.
sn The water. The text deliberately changes now from the term for the watery deep to the general word for water. The arena is now the life-giving water and not the chaotic abyss-like deep. The change may be merely stylistic, but it may also carry some significance. The deep carries with it the sense of the abyss, chaos, darkness—in short, that which is not good for life.
(The acronym tn stands for "translator's note" and sn for "study note".)
So there are are actually two uses of water imagery in the text. The first specifically relates to the ocean, which is a symbol of death (see Jonah 2) and the second is plain water, which can be a symbol of life (see Psalm 107:35).
On the other hand, the words are sometimes used in parallel to mean the same concept:
From whose womb does the ice emerge,
and the frost from the sky, who gives birth to it,
when the waters become hard like stone,
when the surface of the deep is frozen solid?
—Job 38:29-30 (NET)
Jonah's poem also uses מַיִם (mayim) to signal the dangerous situation he is in; the water is going to drown him without divine intervention. So we need to look at the context of Genesis 1 to understand what the author intends by the word.
Life springs from water
The creation account abounds with life and water is a critical component. The water doesn't contain life yet. Verse 2 hints at the general arc of the creation narrative: emptiness transformed to abundance. The Spirit of God hovering over the deep prompts the author to shift from desolate imagery to imagery with the potential for life. The same word is repeated in verse 6 (thrice), 7 (twice), 9, 10, 20, 21, and 22. Day 5 is particularly striking:
God said, “Let the water swarm with swarms of living creatures and let birds fly above the earth across the expanse of the sky.” God created the great sea creatures and every living and moving thing with which the water swarmed, according to their kinds, and every winged bird according to its kind. God saw that it was good. God blessed them and said, “Be fruitful and multiply and fill the water in the seas, and let the birds multiply on the earth.” There was evening, and there was morning, a fifth day.—Genesis 1:20-23 (NET)
Clearly, the water sustains life! Meanwhile, the first word (תְּהוֹם "deep, sea, abysses") does not show up in Genesis until God uses in to destroy life in the days of Noah. The context shows that "the water" in Genesis 1:2 is a symbol of life.