Outside of blurry photos, shaky videos, and alleged "eye-witness testimony" what proof is there UFOs exist?
There are mountains of eyewitness accounts–which count as circumstantial or indirect evidence. But beyond that, there is also a significant body of sensor evidence from military and civilian systems, including radar tracks, infrared/FLIR footage, and multi-sensor corroborations. These provide stronger circumstantial or indirect evidence than testimony alone, though they still require inference to interpret.
There is no publicly confirmed material evidence (direct evidence)–such as recovered craft, biologics, or exotic materials of non-human origin–that we know of.
That said, whistleblowers claim the government possesses such material (direct) evidence, but those claims remain unverified and are themselves more circumstantial or indirect evidence at this point.
Evidence of what, exactly? That has yet to be determined.
It might be mass misperceptions, psychological phenomena, or expectation bias. It might be advanced human technology (classified or foreign). It might be something metaphysical or spiritual. It might be mass hysteria. Or it might actually be exactly what some witnesses and sensors appear to show. It could even involve something or someone (possibly a non-human intelligence) interacting with or tampering with human perception and technology.
The point is, we just don't know. But that uncertainty doesn't mean we should rush to conclude it is 'nothing.'
The one thing we do know is that something is going on. There wouldn't be this mountain of anecdotal, eyewitness, and sensor-based circumstantial evidence otherwise. Many of the highest-quality cases involve multiple trained observers plus independent sensor data that defy easy explanation–which is precisely why serious scientific and national-security investigation continues.