Not necesarily. Scientists are currently studying plants that grow without sun at vents in the earths crust and plant like organisms that feed on minerals in the earth.
Theologically speaking, I believe the first light was not the light of the sun but rather the light of Jesus. (See John Chapter 1) In addition in Revelations the new earth is lighted by God not by the sun. There is no need for the sun anymore to light the city.
Scientifically speaking, it wouldn't be the light of the first sun, but the light of the explosion that started the Big Bang.
Theologically, I'd say the Light of God, but the Big Bang could be the physical manifestation of the Light of God.... I haven't really thought about it, though, one way or another.
Hey, God did it; it's His light.
The Rabbis used to teach it was the light of Messiah. I believe it is what we call "Shekinah." In any event, the very next thing G-d did was separate the light from the darkness. IMO: the separated dark place is hell.
Shalom.