The distances are indeed vast, but the time periods involved are yet more vast. A Von Neumann probe travelling at quite modest speeds should be able to spread

The distances are indeed vast, but the time periods involved are yet more vast. A Von Neumann probe travelling at quite modest speeds should be able to spread over our entire galaxy in mere millions of years; the universe is billions of years old. So while direct visitation by aliens seems highly improbable, such a probe making contact seems at least a theoretically plausible possibility.