to expect an alien civilization (assuming a lightspeed limit) to magically show up on command when you want or expect them to
This statement betrays a misunderstanding of the Fermi Paradox. I don't expect them to show up now, today, or tomorrow or in 100 years.
Moving at a tiny fraction of the speed of light, and allowing perhaps a thousand years after a colony is established before they send out a colony ship of their own, it would only take a couple million years to colonize the entire galaxy. How many "couple million years" opportunities have there been in the billions of years that our galaxy has been around? All it takes is one space-faring civilization to evolve in all that time, and a few million years later, you'll have colonies on every single star.
The Fermi Paradox does not ask why aliens do not magically show up today. It asks why they haven't been here for a billion years or more.
Why aren't there monuments all over the solar system? Why aren't they living in asteroids or artificial habitats in solar orbit? Why don't we seen the ships that make their economy work buzzing around our solar system? Why don't we detect the heat signature from their industry? Why don't our SETI searches pick up radar pulses from their asteroid and comet detection systems (the most powerful beacon we send into space is PAVE PAWS, which a SETI program like our own could detect from 400 light years away). We've been to the moon just ten times, and five times we've left part of the spaceship in solar orbit (the Saturn IVb upper stage) yet amateur astronomers sometimes discover these spacecraft (see J002E3 as an example). If it's that easy for us to spot derelict spaceships, why haven't we spotted the thousands of them that must have been left behind during the billions of years that all those alien civilizations have been visiting us?