To be honest i think life can happen in different areas of space and planets. I dont think space would be infinite. If it were then there must be others living in this galaxy. Im sure earth isn't the only place humans can live on out of billions of planets.
Given we have detected 1800 planets within only a few hundred light years and they have to be specific arrangements and sizes for the detection to work the estimate is our galaxy contains around a trillion planets. Our galaxy is rather typical and there are around a trillion galaxies in the visible universe. That puts the estimate for the planets at around 1,000,000,000,000,000,000,000,000 in just what we can conceivably see.
Space itself sure can be infinite. It is something we can measure directly through the cosmic microwave background (CMB) among other methods. We know the universe volume is a minimum of 50 times larger than what we can see to infinitely large. We may see a better estimate within 5 years because of the discovery of gravity wave signatures in the CMB is going to get a nobel prize for the discovery of inflation and we will see many more experiments focused on this in the near future.
Its just that we can go anywhere in just a split seconds, it takes years and years just to reach a planet near earth. Then it would prolly take 50-100 or more years to go further. There must be an end to endless space.
You know how we are in a galaxy. And in that galaxy is billions of planets. As you go further out of the galaxy you may see more galaxys. Since there are more than 1 galaxy means maybe more than 1 living planet because our solar system has more than 1 sun. There are millions i think but any ways it seems as if you zoom out of our galaxy and you see complete darkness which probably has to end eventually. But what will happen once you reach the end? It will prolly take a million years just to leave our galaxy.
Yes we here on earth are proof that life can arise on planets similar to earth. It's why scientists are looking on mars since it had water and an atmosphere in the past and is similar to earth. But with earth being a relatively common type of planet and something like a minimum of 10^24 planets then it's pretty likely there is even intelligent life somewhere out there and at some time in history.
But like you said we are limited by light speed travel and in fact even that is pie in the sky fast. It's highly likely that we will never see or hear from any even in a million years. It's actually kind of nice to think that even if they exist they cannot get to earth because of the vast distances involved. Makes sure we won't have a real life Hollywood movie on our hands.
As I said in earlier posts interstellar travel is going to be very slow it could easily take a million years just to travel to the far side of the galaxy (70,000 light years) in an highly advanced ship. But it should be possible to travel to the nearest star systems in only a few decades perhaps even starting in just 100 years from now.