@Elhassasdi04 - Cosmic background radiation and the fact that the universe is constantly expanding suggests that it all started at one point (with the Big Bang). I think this answers your question on how the Universe demonstrates properties of the Big Bang Theory. By properties do they mean evidence?
To show that respiring animals produce carbon dioxide.
Set up two test tubes with limewater in each. Put rubber
stoppers over the tubes and metal gauzes inside – one test tube
should have woodlice over the metal gauze.
The limewater in tube with woodlice turns milky. There is no
change in limewater in other tube.
Limewater turns milky, as carbon dioxide has passed into it.
This only happened in tube with woodlice – woodlice
producing carbon dioxide.