Fact: Very few planets we know of seem likely to harbour life. They are also very far away.
1. Send microprobes [with instructions to replicate bigger telescopes at their destination] and relay visuals back to earth.
1a. Create oases at regular intervals outside our solar system, to the nearest likely planets; assume it will take 300 years+ to get to the nearest system.
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1b. Create mini black holes, at long intervals, outside our solar system, to slingshot probes around their gravity wells, to the nearest star.
2. Find black holes, send a micro probe in and see where, and if, it pops out. Timeline: hundreds of years.
3. Study advanced out-of-body techniques to send subjects’ minds to remote-view distant planets.
4. Create a gravity-pinch so a vehicle generating it can be ‘drawn’ at sub-light speed in a particular direction.
5. Find some equation of space/time/gravity/electro-magnetism that allows us to manipulate them in a novel way. Easy!
6. Find some way to ignore current laws of physics, by using higher ones.
7. Collate all known accounts of spaceships. Filter out occult, eccentric and misidentification accounts. Find commonalities in the rest and try to copy the science.
7a. Create miniature versions of any likely-successful craft, for testing purposes.
The Nazis appear to have made some kind of working craft, using unusual propulsion, near the end of the war. The reason they were able to do it is because they were highly motivated, highly organised and looking in a different direction to US/UK scientists; they weren’t inhibited in trying weird ideas.
Contrast that with current Western projects 60 years later; they’re all still based on ‘bottle-rocket’ technology. We’re never getting off this planet by that means.