Pokemon in starting Routes usually have Quick attack.
>When encountered, a wild Pokémon's moveset will consist of the most recent four moves its species learns by level-up
That being said, Quick attack is a fairly common move learned at lower levels, so it should be easy to find one that knows it.
You can look for a Fletchling, Bunnelby or Pidgey on Route 2, or you can find any of those and a Pikachu in the forest just ahead of Route 2.
For example: Fletchling learns it at level 6. Considering that on the first route Pokemon are mostly from level 2-5 it should have it every time.
Hope I helped.