We honestly don’t know. We will forever be stuck in our little bubble we call “Observable Universe” so we will never be able to fully prove the infinity of the universe.
As of now, we have no real evidence that suggest the universe is finite so, many scientist believe that the universe is infinite. But make no mistake, the lack of evidence for one doesn’t imply the opposite. The universe equally can be finite or infinite.
Let’s explore the infinity. What does it means for the universe to be infinite? Like above, we don’t know but we can imagine. Maybe it’s truly infinite, you can travel in any direction and you will always see the same old things, stars, galaxies, nebulae, maybe even life, forever and ever, no matter how far you go. You might even find another you that live the exact same life as you are, in fact, there might very well be infinite copies of you out there…
Maybe it’s only infinite in space, the further you go, the less and less stuff you will find. At some point, you might reach a point where there’s nothing but space left. Does this count as infinite? That would depends on if you consider “space” and “nothingness” something. Personally, if you can still travel pass the border where matter ceases to exist into “nothingness” then that nothingness must be something.
Basically, we don’t know. Contemplating the question might never arrive at any answer but asking and thinking is fun and that’s what human do and will continue to do so, even if it drives us crazy.
Oops, let me stop now before this turn into an essay, we still have finite universe to talk about but since you only ask about infinite, we will stop there.
Edit: Minor typos and grammatical mistakes.
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