Which say the paper tray is at the back. Do you mean the little thingy/shelf on which the prints rest?

If so, try feeling for a small, fold-over tab-like thing of plastic that you can lift and use to pull the paper rest out to its full length.

Edit: This is the online manual for the printer.

https://files.support.epson.com/docid/cpd4/cpd42276/index.html

If you look at "Product Basics" then product parts, TOP, the first diagram shows the location of the Paper Support (Nos. 3 and 4) and the tab I'm describing.

Expected it to get stuck in a paper jam but it went through with no problems and fell out the front on the floor.

Kind of had hoped it would give me another reason to replace this old printer.
Well, guess the front tray is just a 'convenience' to catch the printed sheets.

And a little airing shelf, to let the ink dry. I've never seen one of these stuck inside the printer.

You are in a no loss situation to "persuade" it to open with some gentle prying. I'd suggest proceeding gently to finesse it open first rather than a crowbar as a first try. It is likely jammed at the sides, rather than the top, so some lateral wiggling might free it.

After all, unless you go gonzo on it, the worst thing you can do is to break the tray which doesn't affect the printing.