How can the employer prove a negative?

At most I imagine the plaintiff is allowed to do discovery, and then has to prove positive discrimination based on that.

If you read the document again (?) maybe you'll see it's not about proving a negative. Instead, it's a standard of due care. Did you check whether using some particular tool illegally discriminates and document that consideration? From the document itself:

"Clarifies that, when designing or choosing technological tools, employers must consider how their tools could impact different disabilities;

Explains employers’ obligations under the ADA when using algorithmic decision-making tools, including when an employer must provide a reasonable accommodation;"

If it's a civil case, it's just the preponderance of the evidence. The jury just has to decide who they think is more likely to be correct.

> I am not sure, but if I remember correctly employer must prove they are not discriminating.

That seems backwards, at least in the US.