Possible means could. It does not mean is. For example, it would be possible for me to get in my car and go someplace right now, but the fact that I don't means that me getting in my car right now and driving is not real.
A lot of things are possible without actually being real.
You need to prove something for it to be accepted as real, however you don't always have to prove something for it to be a possibility.
The four minute mile was always possible, but everyone thought it was impossible. Then Roger Bannister did it, and then it was real. That proved that all that time before he did it, it was possible as well.
However, if you can prove something to be impossible, then it is an impossibility.