If you are flashing the same ROM .zip file that was installed previously then you should be able to do so without doing a factory reset in the process. So if it's the same ROM, and if your data haven't already been deleted, this should be possible.
Now I've never heard of OrangeFox so don't know whether there is any quirk in its interface, such as it doing a reset by default when you flash a ROM. The recoveries I used in my ROM flashing days, including the most widely-used one (TWRP) kept such things separate: you just flashed the ROM, and it was up to you whether you did a reset or not. But if you didn't choose to do a reset when flashing and the data were gone then maybe you need to do something special with OrangeFox to tell it not do a wipe (the opposite of what other recoveries do)? Or maybe the data had already been deleted by whatever corrupted your ROM, and so nothing you did could have saved them.
I am however curious about this "recent upgrade": custom ROMs don't generally receive over the air updates, you update them by flashing a newer version of the ROM. So what exactly was this "recent upgrade", and what exactly happened (as this might give a clue as to what happened to your data)?
Of course if you flash a different custom ROM from the one that was previously installed it's likely you'd need to do a reset anyway, since the system data and settings will almost certainly be incompatible. If it's based on a different base (e.g. AOSP vs a manufacturer's own customised Android) or a different major version of Android then you almost certainly need to do a reset.
If you have a custom recovery and don't want to risk losing stuff then take a backup using the recovery every now and then (a "nandroid" backup) and keep a copy on some other device (SD card, flash drive, etc). If your ROM is rooted you can also take full app and data backups: Titanium Backup used to be the go-to app for this, but I think it's not been in development for a while. I've heard that there are alternatives, but as I no longer root I don't keep up with such things.
