How to open a downloaded document on iPhone?

I use the Files app.

After a document has been downloaded such as a PDF, I look through the Files app.

You should have the Files app on your iPhone.

See the Apple articles below:

Use the Files app on your iPhone, iPad, or iPod touch

https://support.apple.com/en-us/HT206481

View files and folders in Files on iPhone

https://support.apple.com/guide/iphone/view-files-and-folders-iphc61044c11/ios

When you download a document, you will always be asked where you want to save the file.

Depending on the Save options, you can choose to save to iCloud Drive, Files app or iPhone.

Start the Files app, tap the Settings icon (bottom right), then at File Browsing ->> turn Folders always first On.

Might be useful for next time.

You can search for a file in the Files app, and also change the appearance of the Files app, as Symbols or List.

You can also search in Books app, if it is a PDF file.

Start up Books and locate the file.