We don’t know that the universe is infinitely large, only that it seems extremely likely to be very much larger than we can observe. We can model it as being infinitely large, which greatly simplifies the models in many ways. That isn’t the same as saying that it definitely is infinitely large.
On to your question, we actually don’t know any of those three properties, but (i) is the one that has the least evidence for it. We have no evidence at all that the universe was ever finite. Our best models don’t extend backward that far. For as far back as we can gather evidence, what we observe is consistent with space having been denser in a technical way that if extrapolated would have an instant (t=0) of zero size and infinite density, but we know for certain that our models break down before that point. Not just in the sense of no longer matching observations, but in the sense of not having a model that is mathematically consistent.
We do have evidence for (ii) and (iii) in the sense that we are unable to observe anything older than 13.8 billion years, and that the universe at those earliest observable times appears to have been incredibly denser and hotter than it is now, fitting very well a model that when projected backward has finite time since a singularity of density. So we can have pretty good confidence that something spectacular happened, and our most sensitive measurements can’t find any hints that it happened even slightly differently or with even microscopically different timing anywhere in the universe we can see.
If the universe was finite and not staggeringly larger than we can see (including “wrapping around”), then we would expect to see signs of it from when everything was closer together. An infinite universe is a simpler model than one of some special finite size that happens to be larger than we can detect, so we go with a model in which it is infinite until we’re shown otherwise.
We don’t know that the universe is infinitely large, only that it seems extremely likely to be very much larger than we can observe. We can model it as being infinitely large, which greatly simplifies the models in many ways. That isn’t the same as saying that it definitely is infinitely large.
On to your question, we actually don’t know any of those three properties, but (i) is the one that has the least evidence for it. We have no evidence at all that the universe was ever finite. Our best models don’t extend backward that far. For as far back as we can gather evidence, what we observe is consistent with space having been denser in a technical way that if extrapolated would have an instant (t=0) of zero size and infinite density, but we know for certain that our models break down before that point. Not just in the sense of no longer matching observations, but in the sense of not having a model that is mathematically consistent.
We do have evidence for (ii) and (iii) in the sense that we are unable to observe anything older than 13.8 billion years, and that the universe at those earliest observable times appears to have been incredibly denser and hotter than it is now, fitting very well a model that when projected backward has finite time since a singularity of density. So we can have pretty good confidence that something spectacular happened, and our most sensitive measurements can’t find any hints that it happened even slightly differently or with even microscopically different timing anywhere in the universe we can see.
If the universe was finite and not staggeringly larger than we can see (including “wrapping around”), then we would expect to see signs of it from when everything was closer together. An infinite universe is a simpler model than one of some special finite size that happens to be larger than we can detect, so we go with a model in which it is infinite until we’re shown otherwise.