The universe is infinite, huh. That's a bold statement. Of what type of an infinity are you referring to? Possible mathemathical infinites such as Pi or do you mean to say the concept of infinity in general and the universe allows for all infinities in a truly infinite state in which everything that exists is everything that could exist and nothingness is just a concept of the mind? Is this what you suggest? If so wouldn't that be a finite ammount of infinities, since without nothingness there is nothing but a finite state of everything that ever was and ever will be, every mathematical outcome of every computation that could ever be and that would have to include nothingness, so is the universe everything finitely or an infinity of nothingness...?
We simply do not know. But as of right now, everything points to the universe being infinite. It's flat as fuck and just goes on and on and on and on. We will never know as out view of the whole thing is limited and it is probably expanding faster than our horizon.
But then there's quantum physics. They tell us that there is no such thing as "nothing". Even in the most perfect vaccum we have ever observed, there is still some kind of activity. Weird virtual particles popping in and out of existence, defying the very fundamental rules of space and time left and right. We do not know why that happens and we likely never will. But never has there been any sign to believe that it is even possible for "nothing" to exist.
Let's not even talk about multidimensional multiverses or tachyon worlds where everything is faster than light but can't be slower. It's all a possibilty but we will most likely never be able to see such things as they do not interact with our world in any way. Same as Dark Matter and Dark Energy. The only thing that seems to be universal for everything out there is gravity. And that is way too weak to deliver any real proof.
If the universe is infinite or not is one of the many final questions we will probably never be able to answer. As of right now, you can say what you want, but you have nothing whatsoever to back up your claim. Sure, there's the big bang, but who says there has never been anything before that or in another location? A big bang could happen inside a black hole for all we know. We ourselves could be sitting inside a black hole inside an even greater universe without the chance to ever take a glimpse outside. Those are all very real probabilities discussed by physics and philosophers.
As for aliens, there is bound to be life out there. But we will most likely never see it. The universe is just too damn big in both size and time. Think about it, how long does an advanced civilization exist? 1,000 years? Maybe 10,000? Now put that into perspective of the universe. Those time frames are literally nothing in the cosmos. If our most advanced spaceships would travel that long, they would barely reach the next star. Also, there is the problem, that different civilizations lack any kind of real causal connection. When you are lightyears apart, the concept of a "same time" breaks down completely. You can't communicate, you can't see each other, you don't know what the hell is going on on the other star right now. It has no meaning to us. It makes no difference to us if Andromeda is crowding with life or not. All we would possibly see are civilizations who are dead for millions of years by now.
We know next to nothing about 99,99 % of the universe, so assumptions of any kind are pretty pointless. It's fun talking about it, but you just can never be sure about anything. But saying there is no alien life is like taking a spoon of water from the ocean and say "Welp, no fish in here!". I forgot who made that quote. It wasn't me.