Can humans achieve interstellar travel with the current technology and understanding of the universe? No.
Can humans ever achieve interstellar travel? Maybe. Maybe not. We don’t know.
At this juncture, it is impossible for humans to travel between stars. Our technology is nowhere near that. We have not even been close to our own star, the Sun, let alone any other star millions or billions of lightyears away.
However, to say that we will never be able to achieve that will be a bit premature. Our space travel journey is still at its infancy and nobody knows what a few hundred years of scientific achievement can achieve. To put things into perspective, it would have taken a message to reach from the USA to India at least two to three years just two centuries ago. Today we can do that in milliseconds via the internet. Therefore, it is very possible that humans will invent something in a few centuries that will be able to do interstellar travel.
Having said that, doing interstellar travel is no joke. The universe is huge beyond human perception and it is expanding at an enormous rate. Galaxies are moving away from each other nearly at the speed of light. The closest star system to earth after the sun are the Alpha and Proxima Centauri which are about 4.637 light years away. The fastest spacecraft that we have today will take more than 100,000 years to reach there. Even if humans of the future devise a spacecraft that can travel at 1% of the speed of light (which is more than a billion kilometres per hour), we will reach there in about 430 years. Sounds tough, doesn’t it?There are other factors too that seem to point that interstellar travel may never be possible. For one, our knowledge about space and problems related to it is extremely limited. Maybe, for some reason it is impossible for living organisms to travel in space after a certain point. Maybe, our laws physics do not work in certain parts of the universe. There can be a million other reasons.
Therefore, it is impossible to say whether interstellar travel can ever be possible. In our current situation, it seems pretty unlikely, if not impossible. But a lot can change in a few hundred years.