In Alpha Sapphire, on Route 102, I caught a Ralts that I want to use because its Modest and has Trace. Unfortunately, it only has Growl, which isn't damaging, so am I able to train and level it up?
Yes. To level it up, you can:
Do switch training. This means you put Ralts in battle first, then immediately switch it out to a stronger Pokemon so it gains experience.
If you have it, use the Exp. Share. It gives Ralts a bit of the Exp every time you win a battle.
Stuff it full of Rare Candies. This isn't the best option, as Rare Candies are, well, rare.
Battle with Ralts itself. Run out of PP for Growl, and Struggle your opponents to death. This isn't a good idea, as the amount of healing you will need to do will waste time.
Stick it in the Daycare until it gains levels. Each step you walk is one experience point for Pokemon in the Daycare.
So yes, you can successfully level up a Ralts that only knows Growl. Hope I helped!