Starting 10 billion years after the universe started. Very reasonable low end assumptions indicate millions of years to colonize a galaxy not even 1 billion years. There is also no reason to assume active efforts to communicate. If they had colonized the galaxy they would probably be near enough for leaked signals to be theoretically detectable, although I'm not sure yet whether we have the actual capability to detect such. I think the Allen array will have that power.

The only way around Fermi's paradox in my view is to propose a realistic explanation why a technological species would remain solely on their home planet or that no others exist in our galaxy. It doesn't make sense to me that an intelligent species would stay planet bound given not only the rate our civilization consumes resources, but the rate that consumption is increasing. I think the three laws are a good working hypothesis. I do see a way around it and the expansion issue though. Technology is a double edged sword. It may be quite possible that most technological species destroy themselves before they become adept at spaceflight especially if they are not gifted by nearbye worlds easy to explore such as the Moon, Mars, or NEOs. The increasing consumption of resources may require either expansion into space or a phase change like the evolution of our intelligence or agriculture into a civilization capable of a steady state or at least close to it existence or a far more peaceful nature in order to retain their advanced technology without destroying themselves. The thing is even if that is the norm, only one exception could sweep the galaxy.

Regards,
Mark