I have a friend who owns a house in Montana. His fridge is on an AFCI breaker that trips every time they have a power failure. In Canada, we don't AFCI fridge plugs. Do you not have an exception for fridges?
There are rules about how to do it but generally yes you can use a device type AFCI in the first outlet on a branch circuit if it is less than 50' away (wire length). The easiest way to comply is to use a piece of MC cable between the box and the panel. If it is a straight shot you could even use a piece of EMT or a close nipple for a side by side install. It just has to be in metal. Before I did all of that I would try it on a GFCI only circuit. If that trips look inward toward the fridge. It is not uncommon for old fridges with bad compressors to trip GFCIs.