My answer would be YES and here’s why…
Let’s assume that we are talking about carbon/water based life like that on the earth rather than something exotic such as silicon based life, carbon/ammonia based life, machine based life or plasma/energy.
For life to exist and evolve to intelligence we would need:
(1) turns out to be quite common. Lets be pessimistic and assume only 1 in 10 stars have these. Since our fairly average galaxy has about 100 billion stars that would mean 10 billion candidates. Stars left - 10 billion
(2) seems to be very common. In fact astronomers believe there are few first generation stars left. They’ve all exploded scattering their mass to form second generation stars. Stars left - 10 billion
(3) will cut down the number of aliens considerably. Half of them will have been destroyed by ELEs. Stars left - 5 billion
Given planets forming in the Goldilocks zone around second generation stars you can fairly safely assume their atmosphere ill be similar to that of the earth. Let’s be pessimistic again and assume only one in five is like that. Stars left - 1 billion
The atmosphere of water vapor, carbon dioxide, chlorine and sulfur compounds, methane, nitrogen, and ammonia would have started to react under the influence of heat, visible light and ultraviolet light and radiation. Amino acids would have formed and dissolved in the oceans condensed from water vapour. Again under the conditions available those amino acids would have reacted and combined in a myriad of different ways. The possibility of a living organism being formed as remote BUT this possibility existed for 2 billion or more years. It’s almost inevitable life starts.
Now it starts to evolve, still being changed by the conditions experienced. There’s plenty of food available in that soup of amino acids in the ocean. Hundreds of times ELEs will extinguish some of it but once life has formed it’s hard to totally destroy it. In fact some might even be splashed into space and survive to seed life somewhere else.
So there are about 1 billion stars in our galaxy where life could evolve and form intelligence. There are 2,000 billion galaxies that we can see!
So we have 2,000,000,000,000,000,000,000 available planets probably with alien intelligence - or do you think we are alone in space?