How do we know what his purpose was or even if he did make the access card? The only way I know of is for the defendant to be charged with that crime and evidence is put on and then the jury decides unanimously whether or not the evidence supports a guilty verdict for that crime.

Right. Which is what happened here. Trump was put on trial, and for him to be convicted the jury had to decide unanimously that the evidence supports a finding that he intended to commit a crime.

Note that in the example above, making an access card is not itself a crime, and since the other guy never went through with it there's no basis for charging him with the robbery. That's why the prosecutors have to prove intent as part of the trial against the guy who falsified the business records (if they want to support the felony, rather than the misdemeanor, charge).

BTW, the way you would "know what his purpose was" is the way that intent is typically proven - by circumstantial evidence. For example, returning to Bob breaking into his ex-girlfriend's apartment, if he had spent the day before talking to his buddies about how his ex-girlfriend had just come into a lot of money, and that he knew that the money was in her apartment, and that he was having some financial difficulties....you would use that to prove up a charge of attempted robbery, and try to convince the jury that the reason he broke into her house was to steal that money. You can't prove what was literally in his head at the moment he broke in, but you can assemble enough circumstantial evidence to eliminate reasonable doubt that he was motivated by anything else at that point.