Missing data folder

I have an .aup file but no data folder to support it. Where might the data folder have gone? Is there a way to recover?

The recycle bin?

Not without the data.

If Audacity did not close down correctly and that was the last time that you had Audacity open, the data may still be in Audacity’s default temp folder, in which case when you launch Audacity it will either, see the old project and offer to recover it, or it will find a load of “orphan block files”.
If Audacity offers to recover, say Yes, then when recovered, use “File > Save As” to create a new copy of the project (new unique name).
If Audacity finds a load of “orphan block files” do not delete them. Make a copy of the Audacity temp folder and put the copy somewhere safe. It may be possible to put the AUP and the data back together. The location of Audacity’s temp folder can be found by looking in “Edit > Preferences > Directories”.