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It is inconceivable that among the 10^24 stars in the universe ours is the only planet to host intelligent life. It is also inconceivable that we'll ever meet that life. Cosmic distances are just too great. Slightly more possible that we'll detect intelligent alien life through, for example, radio signals. But that too is tough. Radio waves obey the inverse square law and that means that a 100kW radio transmission from 1,000 light years away will be difficult to separate from noise. It is also likely that intelligent alien life rises and falls. If we received a radio signal from a civilization 1,000 light years away (roughly 1% of the distance across our own little galaxy) and responded to it, they would receive our response 2,000 years after their original transmission.
The Drake equation framed the odds pretty well. Best estimates say that to believe we're the only technological civilization to have ever existed, the odds of such life arising on habitable planets would need to be less than 1 in 10^22. I've gotta believe we're not the only one. Though for the reasons you mention, it's pretty unlikely we'll ever engage with them. Unless, of course, our understanding of physics is still missing something fundamental, which it likely is.