You can place all the PDFs into one folder, or you can keep them in the same groups of folders that were in your download. It all depends upon how you want to store your PDFs.

Here are the steps for using the Advanced Search. 

Press Shift+Ctrl+F

or

Edit menu item > Advanced Search

1. In the search box, select All PDF Documents and then select the folder where your PDFs are located
2. Enter the search word in the text box
3. Check any of the checkboxes, if desired
4. Click the Search button

This will search through all the PDFs that are in the selected folder. If you keep your PDFs in the same folders that were in your downloads and then place those folders into one, then you will be able to keep the browsing for folders to a minimum.