Much like the idea that life has the ability to develop independently in multiple locations throughout the Universe, coupled with the belief that some of the simple celled life that develops will have the ability to become multicellular, and potentially evolve into an intelligent civlisation.
As mentioned in the argument "Independent Development of Simple Life", this belief states that the necessary condition for simple life to develop are abundant throughout the Universe, and are frequently mixed in the correct combinations for single-celled organisms to form. The most common way to help estimate the number of intelligent civilisations in the Universe is the Drake Equation. Which uses a number of factors, many of whose values we know accurately, with a few still though require a lot of highly contested approximations. The equation: N=R* x Fp x Ne x F1 x Fi where N=Number of planets with intelligent life R* = Average Star Formation Rate Fp= Fraction of Stars with Planets Ne= Average number of planets that can support life per star F1= Fraction of planets that go on to develop life Fi = Fraction of planets that go to develop intelligent life There have been a large variety of estimates for the fraction of planets that have developed simple life to then evolve more complex and intelligent life, commonly termed the Fi factor, The range of values for the fi factor has a massive range, but it is often not quoted as 0. Simon Conway Morris, a Palaeontologist and Evolutionary Biologist estimate the value of the fi factor to 1, believing that it is extremely likely that life tends towards becoming intelligent. Though even if the value was 0.01% of his value, the Drake equation predicts that there would be 15,600 intelligent civilisations in the Universe.
Though Amino Acids have been seen to naturally develop in the lab using what we think was contained within the "primordial soup", not only have we never seen these Amino Acids develop into far more complex molecules. Not only this, but we do not know for sure what was contained within the "primordial soup", it is purely speculative. Even in space within the giant molecular clouds, we have not observed anything more complex than simple Amino Acids. We have also never directly observed Amino Acids on any planets, let alone on planets contained within an orbit that we classify as suitable to life similar to ours. The value for life that evolves into intelligent life is 100% speculation. There are also a huge number of estimated values that put us as the only intelligent civilisation in the Universe.
There is significant evidence that life can form in other places in the Universe. The universe is so large and has existed for so long that even if the fraction of planets that can develop life and then develop intelligent life is incredibly small, the number of intelligent civilsations in the Universe is on the order of tens of thousands.
Rejecting the premises
Though there is significant evidence, a large amount of it is still speculation where almost every opinion is highly contested by large percentages of the scientific community. The age & size of the universe being = large is something we do not know factually as true. Relative to the size of the Earth, and to how long humans live it may seem large, but we have no absolute reference point to make this claim factually correct.