Hi 🙂 Great question… to be honest we really don’t know!
Because light takes time to travel from one place to another, light from very very far away is still reaching us… we call the bit of the universe that we can see the ‘visible universe’… at the moment we can’t really tell what is beyond it!
We do know that the universe is expanding though … kind of like a balloon being blown up … 🙂
The trouble is there is no way of checking so people have developed various theories but how can they be checked? We know that space is vast but whether it is infinite depends on what infinity is and we have trouble coming to grips with that because we have no proper way of visualising it.
Imagine a long strip of paper sellotaped into a loop and imagine this is a 2-dimensional (totally flat) featureless world. If you were an inhabitant on that world and started walking along it – as far as you would be concerned it would go on for ever because you would have no way of looking outside and seeing the shape of your world. We are a bit like that with our universe.
If, instead of making a simple paper loop you put a half twist in it before sellotaping it, you get a “moebius strip” and you have now created a world with only one dimension. You can show that by drawing along the loop – you can write on what were both sides of the paper without ever lifting your pencil off the paper. It only has one surface Try it!!