Wasn't part of the Fermi Paradox that a bunch of scientists got together and found that you needed super duper extraordinary evidence that aliens hadn't visited earth; because a civilization capable of building any form of self-replicating exploratory drone would have been able to map our entire galaxy in less than 1,000,000yrs, assuming a speed of 0.1c?
Iirc the fact that we haven't found a probe, interstellar message, colony ships or artificial extraterrestrial satellites yet is the super duper extraordinary evidence that supposedly disproves their existence. Our galaxy alone is so huge that the fact that there aren't aliens is the weird part.
Also, part of the reason why exploring the galaxy would be so slow is because humans are too scared of nuclear engines. We're literally shooting ourselves in the foot when it comes to space travel because we're too paranoid of nuclear to find a safe way of getting a nuclear engine into orbit. Nuclear engines would dramatically reduce the travel time not just within our system but also other systems to something reasonable.
Iirc a nuclear rocket would cut travel time down to centuries between stellar systems. While cruising the galaxy in one go might not be feasible, travelling to a nearby system would be.