Yes, God gave the sign of the rainbow. The text does not say that He created it at that time, nor what the design signifies.
Further, your quotation proves nothing regarding your incorrect assertion.
i believe HE created rainbow
after the Great Flood = Genesis 9:8--17
Then God spoke to Noah and to his sons with him, saying:
9“And as for Me, behold, I establish My covenant with you and with your descendants after you,
10and with every living creature that
is with you: the birds, the cattle, and every beast of the earth with you, of all that go out of the ark, every beast of the earth.
11Thus I establish My covenant with you: Never again shall all flesh be cut off by the waters of the flood; never again shall there be a flood to destroy the earth.”
12And God said: “This
is the sign of the covenant which I make between Me and you, and every living creature that
is with you, for perpetual generations:
13I set My rainbow in the cloud, and it shall be for the sign of the covenant between Me and the earth.
14It shall be, when I bring a cloud over the earth, that the rainbow shall be seen in the cloud;
15and I will remember My covenant which
is between Me and you and every living creature of all flesh; the waters shall never again become a flood to destroy all flesh.
16The rainbow shall be in the cloud, and I will look on it to remember the everlasting covenant between God and every living creature of all flesh that
is on the earth.”
17And God said to Noah, “This
is the sign of the covenant which I have established between Me and all flesh that
is on the earth.”
IMHO - The rainbow reflects the truth of the firmament that separates the waters above = thus its creation and meaning to us on earth.