Is it normal to live in a paradox?

This is actually often discussed.
Existence is possible, because we actually do exist.
Although many things in nature do exhibit a cyclical behaviour, all these cycles did have a beginning at some time. Cycles do not continue endlessly, but change through spacetime. One example of this is: The Earth-Moon system. At some point in the future, The Moon will escape the gravity of Earth.
You do not understand time properly. Time is, quite simply: a property of massenergy in space. A clock is not time. A clock is an instrument designed to measure time, usually as a portion of the time that it takes the Earth to complete one orbit around the Sun.
The cycles began at the very beginning of the formation of the Universe.
Aliens do exist in nature, god does not. 'God' is an abstract concept. What created aliens was (and is) an evolution of massenergy and sometimes quarkenergy, sometimes quite similarly to our own evolution, but sometimes quite differently. 'God' was created in the minds of humans (loosely). [Some other human species also created a concept similar to 'god']
Space is infinite and always existed. It is not like a little piece of paper.
Space was never 'blank'.