An incredible coincidence or else she somehow happened to know where he would be to meet him like that.
If it was set up, then why play hard to get?
And if it was set up, was she using him and if so, how?
My take- Everything revolved around Szell being paranoid that everyone was out to get his diamonds, and having a support team of agents/assassins/goons/honeypots that were basically supernaturally skilled at tracking targets and correctly anticipating their every move.
Doc was an American spy who used Szell as an asset post WW2 to hunt down Nazis in hiding. Doc knew everything about Szell, and Szell knew Doc knew everything. He assumed anyone who knew about the diamonds would try to take them, including Doc. Therefore Szell and his team were thinking 20 steps ahead and had things in place for every single possible contingency imaginable, including maybe at some point it could be handy to be able to manipulate Doc by threatening Doc's little brother Babe.
Elsa was working for Szell from the get-go. She played hard to get to avoid suspicion. If she was too easy or came on too strong, Babe might have figured her out much sooner. IMO it was obvious Doc more or less knew she was working for Szell, but he couldn't come right out and openly say it, so he had to give Babe the b.s. line about her trying to get citizenship.
Clearly a setup, as you say. Elsa admitted as much at the country house near the end of the film. This was known even earlier after Doc outed her as a fraud at lunch, and Szell implied the same soon after when Doc confronted him about involving family.