There’s two tricks I have that work pretty well for me.

The first is like the advice from Hitchhiker’s Guide about the secret to flying is to throw yourself at the ground and miss. Think about the problem long enough to get an idea about where the trouble is coming from, then go do something else, like take a shower or work on something else. Don’t watch tv - that will fuck it up - but basically it’s distracting your conscious mind to give your subconscious time to work on it without being bothered. When it comes up with something, that’s when you’ll become aware of it. Going for a nature hike or bike ride is also a great approach.

The second is to try to prove the opposite. Try reversing the argument and say “such-and-such is impossible” and try to build an argument around that point. When I do that, it makes the other part of my brain - the annoying and iconoclastic part - say “But what if…” and the answer might lie somewhere down that path.