Well, there is 1 RNG advancing NPC outside of Elm's building, so you have to get her to advance the frames for you, than be able to get into the building before she advances any past what you want.
Since there is no other way to advance the frame, having a really low frame helps. And/or having a frame matching that of the starter you want.
My frame was 31 so I advanced the frame using the NPC (wearily, she kept skipping my frame, as she seemed to move 2-3 spaces per time she moved) till 23, than ran inside and picked up Totodile thus came out that special little thing.
I am unaware of how to do it on a cart, as you can't keep tract of frames. I suppose you could make guess work that she skips frames 3 times every time she moves, but the soft reseting for the delay + attempting the frame wouldn't make it worth it.