We've had life for about 500 million years on earth. Maybe a billion as single celled life forms. I used to worry that in 5 billion years it'll all be over on account of the sun entering a new phase and engulfing Earth. But it appears in about 800 million years photosynthesis will no longer be possible [1], which puts an even closer limit on our time here. There's a good chance some will get off this rock, but many won't. And all that we know will be lost, and we'll need space suits to visit, no more nature to enjoy, just barren rock. We'll not be us anymore either of course, time will tell what we evolve into.
You're right though; our time here is very short and if we want to ensure survival of Earth-based life then we need to start considering panspermia, first to other planets in our own planetary system (assuming they don't have native life already -- we're not entirely sure about that yet), and then to other systems.
If we can colonize a world around a red dwarf, preferably a young one, then Earth-based life should be set for billions of years into the future.
4.5 billion years until by the laws of physics a state emerged, where macrobodies consisting of billions of cells, fueled by exploitation of energy from chemical reactions, are using movement devices that employ triggered explosions, and are constructing machines which assemble elements on atomic level in such way to make apparatuses which enable the harvest of information by the laws of logic.
I don’t know, people. Maybe I am turning pessimistic, but it took the universe in between a third and a half of its duration of existence to produce a system which yields mass produced RGB keyboards, failed SpaceX launches and climate destroying lifeforms. I would estimate the probability of another biogenesis happening in parallel to ours is very low.
On a single other planet? Very close to 0. But multiply this number by say 400 billion for our galaxy, and maybe additional 150-2000 billion for all the galaxies, and the chances are not that bad. Probably.
Plus the idea that life needs to look the same as here on Earth has no logical base - it could be from number of other elements, forms etc. Basic premise is just multiplication, where it goes from there is anybody's guess. Carbon with water is convenient but its not the only option.
Silicon has been suggested as an alternative to carbon as basis for biochemistry. Ammonia-based life has also been suggested (and is also a rather common sci-fi trope).
It took several billion years for the stars to form, blow up, and fuse the elements into heavier and heavier elements that then formed our galactic neighbourhood, our sun and ultimately Earth. Then it took more than 4.5 billion years for Earth to cool, develop life (or get contaminated, if it was panspermia) and evolve that life to a point where it split the atom and built a planetary communications network that allows ordering pizza from any single point on the planet's surface.
I'm certain this process could have been quicker elsewhere, and there's no reason to believe life could not develop under different circumstances, but it's definitely plausible that extra-terrestrial life -- assuming it exists -- is a rare thing and that any alien civilizations may be few and very, very far in-between. On the other hand, the Universe is a rather big place, and even if there's just a single species who reached space in the entire galaxy, that still leaves us with the possibility of life elsewhere.
"A long time ago, in a galaxy far away" is quite fitting. Other technological civilizations could have developed, risen and fallen and crumbled into dust while life on Earth was nothing more than a bunch of proteins chilling in a hot spring.
On the ther hand, it implies that if at some other place these processes happened 1% more quickly, or started 1% earlier, then that civilization would have had tens of millions of years head start to us; they'd have rocket launches back long before Earth had its first primates
It indicates that if we ever meet someone, it's extremely unlikely that they'd be of remotely comparable tech level, more likely they'd be millions of years behind in evolution (i.e. pre-intelligence) or millions of years ahead in technological development i.e. something that's hard to imagine, our fantasies are mostly about extrapolating a millenium of actual novel development.
If you’re worried all will be lost, perhaps focus on how we can make sure Information survives for a thousand years as a first step. It’s really not so trivial.
[1] https://en.m.wikipedia.org/wiki/Timeline_of_the_far_future