Science works by preponderance of the evidence... the same standard as most US civil law...
It is more likely true than not true.
This is coupled to...
We have failed to disprove that this is true.
99% of the new science done in the last 30 years has been by complex inference ...
People can't see atoms... but most accept they exist.
People can't see brain chemistry... but alter it, and its effects can be detected.
We can't see gravity, only its effects. But we accept that it exists as a property of matter.
We can't see most worlds with current technology... but we can detect the motion to within ±1m/s accuracy (and ±0.05m/s granularity or better). If a jupiter class world were orbiting Alpha Centauri at jupiter's ~8 AU, we'd be hard pressed to detect it by any means other than direct interferometry while in a particular two 60-70° wide chunks of its orbit... It's too small to generate the radial V we're able to accurately detect at those distances.
Many of the candidates are cases where we see the wobble effects, and when we add them up, we come up with multi-jovian subsolar masses being the singular most reasonable explanation. By preponderance of the evidence at that point, the community generally will accept them as proven.
One of them, Jeff Marci commented about. It took his team months to realize that the complex wobble was 3 superjovians... they finally worked out the math, and found that only one solution fit the data... and it wasn't simple measurement error.