this would be a long one to be precise, hence i try to make it short.
- take the age of the univers
- discount the time needed for metals to be generated and spread throughout the univers
In astronomy, metallicity is used to describe the abundance of elements present in an object that are heavier than hydrogen or helium. ... These became commonly known as Population I (metal-rich) and Population II (metal-poor) stars
- discount the best-case number of years necessary to develop intelligent life
- discount the best-case number of years necessary for intelligent life-forms to develop the technology needed for space travel
- discount the best case number of years to for intelligent life-forms to develop the technology for interstellar space travel.
- discount the minimum years necessary to reach a significant number of potential earth like planets at close to light speed and calculate the time needed at realistic velocities how they are possible today or are at least a possible future technology and be aware that the fast the journey will be in your assumption the more time you will have to calculate for the time needed to develop the underlaying technology.
If you make above calculation only half very seriously, you will reach a result that tells us that there cannot be any UFOs visiting us, showing themselves on one hand but avoiding contact on the other hand.
All this can be considered proven to be not possible on the given time scale and that said, we can sit down and search for realistic explanations for all the unexplained stuff the makes some of us think that extraterrestrial life forms in space ships (aliens) are and have been visiting us for and since centuries.
I repeat, calculate minimum time needed and put the result into relation with the development of the universe, how many solar life cycles are necessary to provide the necessary elements, create rocky planets, create life on those and develop that life to a level that can achieve all that's needed to travel that long and that far and even then they can't be here at realistically achievable speeds.
Also you have to put into account that the faster a spaceship travels the heavier it becomes and then the thing has to be decelerated in time, over thousands of years to reach a manageable speed close to the target and then the target has to be KNOWN on launch.
As sure as I am that there are probably many many other life forms populating the universe, as sure am I, (and of course others who prefer maths and physics over wishful thinking), that even though aliens (life forms) most probably exist, they can't be here yet, even in case they would be on their way for a few hundred thousand years by now