How can I find the first receptacle in a circuit?
There is no magic method. You disconnect an outlet and see which ones are still live, if any. You don't have to disconnect any that went dead when you did one of the others. When they are all dead, you have the most upstream outlet on this circuit in this room. If the circuit feeds multiple rooms, the problem becomes larger, but not different.

Be aware of - keep an eye out for outlets with different circuits top and bottom (generally switched one half for room lamps) they can be tricky to figure out if you don't look for them.

Another approach (NOT my favorite) would be to use GFCI breakers instead. Automatically most upstream, but also more expensive and needs to be for your particular breaker panel, rather than the generic GFCI you can put first in line and replace with another generic GFCI when it fails (they do fail.)