You will probably be making your case to an insurance company, not a court of law, so you don't need legally perfect "proof" of anything. You'll be negotiating informally with the insurance company through letters and phone calls with an insurance adjuster. You just need to make a reasonable argument -- in plain language -- that another person or company was careless ("negligent"), even if there are also plausible arguments on the other side.
For example, in a car accident case, you do not need to present measurements of tire marks or precise angles of collision. Just point out that the other driver hit you from the rear or turned in front of you. Common knowledge of driving rules tells both you and the insurance company who was at fault.
If you make a good argument why the other person was at fault, the adjuster will realize that if the matter wound up in court, there is a good possibility that its insured person would be found legally responsible. Companies usually prefer to pay a reasonable claim settlement sooner, rather than risk having to later pay not only for your injuries, but also court costs and lawyer fees.