We know how we are handling space exploration. We send robot probes. So once you get good at space travel. You set up automated factories on an asteroid and just churn out probes. Scattering them all over the universe looking for radio waves, nuclear explosion and polluted planets.

Imagine what it must have looked like to the swarms of interstellar probe cruising between the stars, when we detonated Ivy Mike or when the Russians detonated the Tsar Bomba. They would all come running like moths to a flame.

https://en.wikipedia.org/wiki/Ivy_Mike

https://en.wikipedia.org/wiki/Tsar_Bomba

I feel I should point out that the civilizations who did this are probably long dead or just don't care what the probes found. After thousands of years they are gone or have moved on. The probes are just on auto pilot.