Any search for mention of “rain” in the Old Testament finds it mentioned only in Genesis 2:5 prior to the rain that brings the Flood in 7:4. Therefore, many scholars assume that God did not use rain until that time–which would also explain why no rainbow was seen until after the Flood (9:13–16), since it is a natural occurrence when sunlight passes through water drops in the atmosphere.
However, as you have noted, the Scriptures do not specifically state that it did not rain before the Flood. Genesis 2:5 seems to be more easily read as saying that God had not yet caused it to rain when He provided the “mist” or “spring” to water the earth. That was before plants and before Adam. But like the plants (Day 3) and Adam (Day 6), the rain could have started sometime during the six days of creation.
The lack of explicit statement in Scripture can also be compared with geological evidence of raindrop patterns in water-deposited, fine-grained, volcanic ash and sandstone beds in the Precambrian layers, which are pre-Flood. Evidence of water deposited sediments in pre-Flood strata also indicates the possibility of rainfall prior to the Flood.
As for the rainbow, the text does not demand that it first occurs after the Flood. It could equally be understood as that which God had already set in the sky and that now He invests with a new function—to signify His promise not to destroy the earth again by a Flood.