You can reasonably 'grind' meat in a processor. Takes a little time and patience but it works. (I do this all the time when cooking on the road. Not about to carry a grinder with me!)
Partially freeze the meat so cutting is easier then cut into 1-1.5-inch pieces. Try to make the pieces a consistent size (but don't go nuts over it). Spread out on a parchment-lined sheetpan and return to the freezer to par-freeze again, about 10 min.
Put your blade in the bowl and put just enough meat to cover the bottom without crowding and process by pulsing on and off till the meat is chopped kind of well, scraping the sides of the bowl periodically. Don't shoot for fine at this point, just chopped. Scrape this into a pile and put on the parchment in the freezer; repeat with the remaining meat till all is done.
Return about 1/3 of the meat to the bowl. If too frozen allow to sit for a few minutes. 'Grind' again, pulsing frequently and frequently scraping the sides down. If the meat gets too warm before it's done it will not chop finer. Scrape to the parchment and par-freeze again. (It's par-freezing that's the key to finey chopping meat.) Repeat till the meat is very finely chopped, mix alll together well, then continue with the recipe.
It's a bit of a process, as you see, but not difficult. Once you do it once you'll get a feel for it - how frozen you want the meat, how much to put in at a time, etc.
Note: Pork shoulder fat is all pretty much soft fat. If using beef, use shoulder (chuck) but feel the package before purchase. Try to avoid packages with substantial hard fat. Get those with as much soft fat as possible. Trim off and discard and hard fat/gristle before freezing the first time.