For plastic boxes, one of the best tools (after the drill for making round holes) is a special file called 'abrafile'. The one I have and use most is round, about 1/8" in diameter and 5" long (3.5mmx125mm), with a plastic handle. Its different from conventional files in that the teeth are very coarse and the file shaft is flexible enough so it won't break if one tries to bend it - it actually bends.
There are larger diameter and also square abrafiles available but the smallest is most useful for the above.
I first drill a hole, slightly in from each corner, and then use the file like a saw to cut the square or rectangular opening. Its quite quick and if one files (saws?) carefully only a little smoothing with a conventional file is required for a professional looking cut out.
These abrafiles also work in aluminium but the cutting is a little slower of course. Sometimes I use my hand 'nibbler' to cut holes into metal boxes. This requires a larger pilot hole of 3/8" (10mm) and the cut is 1/4" (6.5mm) wide. This also does not cut close to the corners of boxes.
Another trick is to drill a close spaced row of small (2 - 3mm) holes all round the opening and file the parts between the holes with a needle file.
this requires careful drilling on a bench drill to be successful. One could also, for straight lines, drill just a few holes in a row at each corner, enlarge them into a slot and then use a hacksaw blade (there are special handles available to hold the blade) to cut along the rest of the marked line of the opening. Try to cut with a 'pulling' motion or the blade is likely to jam and snap.
I do have a few chassis punches but these are expensive for just the odd hole - more useful in a workshop where lots of holes need to be made.
One 'could' also use a hole saw, again expensive, for a quality one (the cheap, multi set- split barrel, variety are a waste of money, IMO, and can be downright dangerous) and holesaws leave a rather rough finish.
There are tools like a 'flying cutter' that do very neat round holes into plastic, this is an adjustable tool, but it only works on a bench drill safely and requires to clamp the box firmly to the drill table which is not possible with small boxes.
When drilling holes with a power drill into plastic be careful as the drill often 'bites' and drags the box out of one's grasp. Countersinking holes is especially tricky and they are easily ruined by a 'runaway' drill bit. The cure is to very carefully sharpen the drill bit but that requires a grinder and the knowledge how to sharpen drills.
I don't have a Dremel tool either and got by with the above suggestions for 40 years, cutting all sorts of openings into project boxes. Mind you, if Santa were to bring me a Dremel...
I hope this gives you some ideas, the burning the hole suggestion is a bit crude, IMO :wink: and bound to be inaccurate, not to speak of the toxic fumes created by this process. But, if you are desperate....