I came across this paper a while ago on Youtube channel:
https://arxiv.org/ftp/arxiv/papers/2004/2004.03968.pdf
There is a lot of complicated math that I don't understand, but some of the points made are interesting.
They calculate, based on the number of stars and estimated planets, that there are/were likely 36 intelligent civilizations in the Milky Way. The number actually ranges between 4 and over 200, but 36 is the number they settled on.
The catch is that based on the age of the galaxy, it is likely that the peak for intelligent civilizations in the Milky Way was 5 billion years ago. They also suggest that from the time that an intelligent species begins exploring the stars, it would take on average 3000 years to locate another civilization and another 2000 years after that to set up 2-way communications. Just not practical given our life spans. Basically, if ancient Egyptians started exploring the stars when the pyramids were constructed, we would be lucky to have finally established contact today. It would be a project that would take 150 generations to complete.
It's based on some assumptions, like the time from when genesis occurs to how long evolution takes to produce complex life, and then intelligent life. These assumptions are obviously Earth-centric, but there are reasons to believe certain biological principles would be universal as they are based on chemistry and physics principles that are universal. It also assumes that a planet where complex life evolves, there will be at least one species that evolves to be human-like intelligent life. Given the number of species that have ever existed on Earth and only one has evolved to that point, it might be a stretch to think that it is likely to occur on another planet. Evolution doesn't have a goal for higher intelligence, it's all about surviving in your habitat. It could be extremely lucky that the habitat here facilitated that once.