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I don't see how a local professor would be out of Pokemon, considering every Professor in the series produces a Pokemon in the intro cutscene. It could be how it was in BW where Juniper goes out and catches a Pokemon for you instead.
>b-b-but the professor can't do that, for some reason
Then literally any rando with a Pokemon can do it, like Dude from GSC. Catching a Pokemon is so easy that even near toddlers can do it, a situation in which you straight up can't catch a Pokemon feels really contrived, especially considering how a Pokeball is cheaper than most foods in universe and a number of Pokemon can be tamed without Pokeballs if you just talk to them nicely and give them food.
The only situation in which something like OP's post could happen is if somehow nobody in the local area owned a single Pokemon.