I’m afraid you have a misconception of how the printer’s cache works. The files are not cached, instead they are sent as 3MF archives when you hit send. The printer then extracts the gcode from the the 3MF archive into Gcode. That file stays on your SD Card forever or until you delete it. Make a note of this because from a privacy point of view, it’s wise to periodically clean your SD card for any models you may not want people knowing you printed such as NSFW models. 
You can then access the files on your SD Card directly from your printers user panel by navigating to the folder and select print. Selecting either the Gcode or 3MF file will work but note that the downside is that this method forces a bed leveling which printing from the slicer allows you to override. I might suggest naming the file to something more descriptive so you can recognize it. Otherwise it will default to the model name. You can change the name by changing the plate name which will override the model name.
You can manipulate the files manually by pulling the SD card and reading it on a computer. Highly inconvenient but reliable. You also have the option of slicing a file in Bambu Studio or Orca directly to a file and placing it on your SD card.
In case you missed it in the slicer, here’s where the Send Gcode to file may be found. You will want to experiment with Export placed sliced file and Gcode file. I tried this a couple of times but I forget which one has the advantage so try both and see which one is easier.
Although I believe the X1 always had SD support from within the slicer, the new Bambu Studio now supports the P1 direct to SD card copy and manupulations in version 1.9 or later assuming you also have the latest P1 1.05 firmware but I found the P1 firmware too buggy and backreved it so I don’t have a lot of experience with that feature other than it worked OK when I tested it.
If you’re using LAN-only mode, the printer supports FTP. I find this to be the best and most flexible option of remotely managing the SD card. But note that LAN-only mode disables handy which I never liked to begin with but you might prefer it, if so FTP is not an option for you. Using an open source FTP program like FileZilla or WinSCP will give you access directly to the SD card without removing the card. It also allows you full access to the SD card as if it were plugged into your computer which the Bambu Studio interface is highly filtered because I guess Bambu either wants to make the experience more user friendly or more likely the case, they don’t want tech support tickets from users who don’t understand FTP. FTP is easy to set up if you have a modicum of technical skills and can read though a half a page of instructions.
Here’s what that looks like in WinSCP. Note that one also can get easy access to the time lapsed videos on the SD card too through FTP without interrupting the printer or Bambu Studio or Orca if you’re in the middle of something.
