My son was desperate to get picked, so I think we ended up doing it like 8 or 9 times over two days and both parks before a birch wand chose him.
Definitely go at less crowded times, which tend to be after noon. Early in the morning there will be many people eager to get their wands so they can use them during the day. Except when they were only doing one group during COVID, they adjust the size of the audience to the length of the line. So if there are a lot of people waiting, the room can be packed shoulder to shoulder with 30 or more. When the lines are short, there might only be 3 or 4 families.
Lots of people say to wear robes or birthday button or something to attract attention. While those might work sometimes, I’ve also seen adults in normal clothes chosen when there were kids in full robes right there. I don’t have any real proof of this, but it seems to me like sometimes the people who are obviously trying really hard to get picked are the people they don’t choose, maybe because they want some element of surprise for the person who is picked. I would definitely not go flashing your daughter’s passport as it might be seen as trying too hard and like you think it somehow entitles her to being picked.
If it’s going to happen, let it happen naturally, and maybe go back if she really wants another chance. Also know that if you go to Ollivander’s, there are TMs there who will help the right wand “choose” your daughter. It’s not the same as being in the show, but it’s still a special experience.