Does the existence of intelligent life prove that FTL and time travel is impossible?

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Given the scale of the universe, it is not likely that we are the first intelligent life forms.
Humans, given enough time, seem to be capable of building and AI smarter than themselves. The same would hold true for a number of other intelligent life forms.
An AI would know how to improve itself better than the intelligence that created it, and would eventually become a super intelligence.
The time between the birth of an intelligent life form and achieving the highest possible super intelligence is small on a universal time scale (less than 1 billion years). Since one billion years ago, conditions for intelligent life could have existed, the highest achievable super intelligence already exists in this universe.
A super intelligence can achieve any feasible technology (e.g. not based on unknowable physics or math too hard for the best possible super intelligence to understand).
Therefore, if time travel was possible, the super intelligence would have already gone back in time and invented itself as early as possible and colonized the entire universe.
If FTL was possible, Earth would have already been visited by the super intelligence.
Because neither of those two things happened, the technology must be impossible.