Yes, but this universe started 13.7 billion ago. We have absolutely no proof of any space or time before then.
Saying the Universe started 13.7 billion years ago just means the universe is 13.7 billion years old. That does NOT equate to the start of TIME. It simply means the AGE of the universe is 13.7 billion years old.
Just because the universe started 13.7 billion years ago does not mean that was the start of time. There was a 15 billion years ago, a 100 billion years ago, and a trillion years ago. A trillion years ago was not the start of time, neither was 100 trillion years ago, or 10,000 trillion years ago.
What you are saying is that because my car is 10 years old, and it started life in 2010, that time started 10 years ago. Don't you see your error in saying that?
If you have no proof of any space or time BEFORE the universe started, then you have NO PROOF of anything before the universe. Having NO PROOF means you can make NO STATEMENT claiming "time started." You want to make that statement then prove it, which you already claimed you can't, because you have no proof. So stop making claims that you can't prove! My claim is the default until it can be shown otherwise. We know time exists, that is a default. To claim it had a beginning requires proof, of which you have NONE!
You can't even talk about BEFORE, because BEFORE means a time prior to, which you claim there is none. It doesn't add up!
You say spacetime is infinite.
I never said "spacetime", that is not a word I use. I use the term "space," which is 3D distance (volume), and I use the word "time", which is duration. Space and time are INEVITABLE, they have no beginning and they have no end. They NEVER STARTED and they will NEVER END. There is no way to end them, and there is no way to start them.
I say only a timeless nothingness can be infinite.
Distance is infinite. Time is infinite. Infinite simply means "continuation."
If you think distance is infinite from the point you are right now, then you are claiming that distance is time, if traveling at the speed of light. If light traveled from your point along a line away from you, it would never reach an "end" distance, and it would travel continuously at the speed of light for infinity, which means it will continuously travel, forever, and not reach an end. It will travel for 500 trillion years and not even be close to an end, because there is no end to distance and time, they are infinite because they are inevitable! There is NO CONCEPT of either of them being anything other than infinite. If you have a concept of them being finite then let's hear how either one of them is finite! Let's hear the concept!
Everything else has a beginning and time emerges with duration of existence.
No! My car had a beginning and it had a point in time for its beginning. There was time before its beginning. The universe is no different! It had a beginning and that was a POINT IN TIME. It's like saying 12:30, that is a point in time. of course there was a 12:29 BEFORE that point in time.
You think because objects have a date of birth that that is the start of time. That is not time, that is a point in time that the object was created! That has nothing to do with duration other than being it's start point! It's like distance, there is a starting point for a 100 meters, and there is an ending point for 100 meters. Do you want to say that space is only 100 meters long because there is a start and end point to 100 meters??