To think that it is impossible is the stretch. To imagine space for all that means beyond even our imaginings is dead is a real stretch.
That's the human condition though isn't it? We think we have to control everything because we're seemingly the higher species on earth. Top of the food chain. Apex predator.
Even when we don't know we broadcast a theory. Maybe we think there is no life in space because our limited level of evolution in the intellect isn't capable of comprehending that life other than what we think it is defined as is possible.
Look at the god topic. We even think we can confine something that is the source for everything we think we know and see fits the mold we imagine and then call faith. It looks like us, in every religion. It has our attitude, in every religion. And in the infinite expanse of whatever is that we don't know or see because we're confined to this third dimensional reality, plane, consciousness, that god we are sure loves one kind of people. The people that define it and then worship it in a religion custom tailored to give it praise. And in return we think that "it" has nothing better to do than obsess over how we sex, how we think, how we dress, and what we do in matters of that praise.
And some are so fixated on subjective controls that they call themselves pagan! And they think that what they think, and do in ritual, makes nature do what they ask.

And she, mother nature, loves them back.

And, when they die she brings them back to do it all over again. And some think that what they do in this life is what makes for that nature, that 'god', to judge them worthy of in shape and identity, when they return.
There are Buddhists, and I was there to see it, who will be excavating a new temple grounds and the contractors are getting paid through the nose for the job. Because the Buddhists there go through ever inch of dirt excavated. Imagine that one for something like a super mall size, and dig through the dirt so as to remove every bug, every worm, every grub, and whatever else alive.
Because, they live and believe those things could be their mom. Or their dad. Or their aunt. Or some relative that was reincarnated there.
Point being, humans think like that. They live their lives like that. They die for that.
And here we are thinking we know that the whole wide expanse of space outside our planet can't have life? Because we don't think so?