The Fermi Paradox

The Search for Extraterrestrial Intelligence (SETI) is an umbrella term for scientific searches for intelligent extraterrestrial life. Scientific investigations began at the very beginning of the 20th century and focused international efforts have been ongoing since the 1980s. 

The Drake equation is an attempt to estimate the number of active, communicative extraterrestrial civilizations in our Milky Way galaxy.

The Fermi Paradox, named after Enrico Fermi, is the apparent contradiction between the lack of evidence for extraterrestrial civilizations elsewhere in the Milky Way galaxy and various high estimates of their likelihood. 

It's based on the assumption that the Big-Bang model is correct, and that life can evolve from non-life by chance (something that has never been observed).

The basic points for the existence of extraterrestrial life are as follows:

• There are 400 billion stars in the Milky Way, of which 20 billion are similar to the Sun.
• Estimates have suggested that one-fifth of stars similar to the Sun have Earth-like planets in the habitable zone (the area with the conditions for life to exist as we know it). 
• If only 0.1% of these planets have developed life, there should be a million planets with life in the Milky Way. 
• The Milky Way is estimated to be 13.8 billion years old (according to the Big-Bang model), but the Earth is estimated to be "only"
  4.6 billion years old. This means that there must have been many chances for life to develop on these other Earth-like planets before it developed on Earth.
• Although only a few of these civilizations have developed
  interstellar travel, we should be aware of them now.
• Even at the slow pace of currently imagined interstellar travel, the Milky Way could be traversed completely in a few million years.
• Since many of the Sun-like stars are billions of years older than the Sun according to the Big-Bang model, this seems to give plenty of time.

By this reasoning, Earth should already have been visited by an alien civilization, or at least by their probes. Since this isn't the case, and 
the lack of evidence for extraterrestrial civilizations elsewhere in the 
Milky Way galaxy, it's seen as a paradox.

There have been many attempts to explain the Fermi paradox; 
mainly suggests that intelligent extraterrestrials are extremely rare,
that the lifespan of such civilizations is short, or that they exist but for
various reasons we see no evidence (rescue devices). 

The Creation Model

The Fermi paradox can be explained by the Bible, see The Creation Model
in The Big-Bang Model Revealed.

Humans are the center of Gods purpose for creation. When Adam fell in the Garden of Eden, it affected all of creation, the entire universe (Rom 8:18–25),
see The Biblical Creation and the Fall of Man. At the end time there will be 
A New Heaven and a New Earth. Earth was created first in the universe according to the Bible. See also The Universe has a Center in 
The Big-Bang Model Revealed. Then it's difficult to assume that God has also created biblical life on other planets. See also time 57:44–59:20 in
"Astronomy Reveals Creation" with Dr. Jason Lisle. 

Note that there is a difference between our definition of biological life and biblical life. Biblical life includes only species that have blood

(Gen (1 Mos) 9:4, Lev (3 Mos) 17:11), and doesn't include plants or microorganisms. But there probably isn't even biological life on other planets. 

My opinion is that only life can create life. Life can't spontaneously emerge from non-life. Pasteurization is based on this assumption, and it works. 

This means that it's reasonable to assume that life only exists on Earth in the entire universe. It can be seen as something that the Creation Model predicts. The Fermi paradox is therefore not a paradox of the Creation Model, but it's a paradox of the Big-Bang model (Isaiah 45:18).

See also Evidence for Creation.