The type of mitres you're looking to do are called case mitres because in a different context they'd be used for casework, i.e. cabinetry or box making1.
Other than sawing them directly (challenging to do with hand tools) the standard method to produce these is by planing. Even if your freehand sawing was very very good and you could do the cuts freehand (or in tall DIY mitre box) you'd still want to finish off the mitre by some method because sawn faces are rarely good enough that you'd want them to show as-is.
Because we're in the era of power sanding you can also do this using a belt sander (or a disk sander for smaller pieces), using a jig of some sort to present the workpiece to the sanding surface at 45°.2
If you do this by planing the traditional jig for the work is called a donkey's-ear shooting board:
As you can see this places the plane flat on its side, as normal for shooting, with the workpiece at an angle hanging off the edge of the bench. More modern planing jigs often approach the problem in a different way, allowing the work to be more easily held steady because it's flat, with the plane angled. Some good versions of this type are shown on the following pages:
Note that you can also plane these mitres entirely by hand, with no jig. It's tricky initially but not too difficult if you mark out carefully and go slow, and as with most things you would get better at it quite quickly with practice. If interested here's a good video on the subject from Mitch Peacock on YouTube:
Many guides suggest the plane to use for this type of work (which would be planing end grain exclusively if you were using solid wood3) is a low-angle block plane. While I consider a block plane an essential part of the toolkit and would suggest anyone (even the power-tool user) have at least one, if you don't currently own a plane I'm not sure it's the ideal first purchase. If buying a single plane a standard bench plane, for smaller work a no. 4 specifically, presents the best bang for the buck and there are a few budget-friendly models available now in most markets that are of quite respectable quality4. Note: if you don't already have any sharpening supplies you need those too right from the start. A plane's iron needs to be super sharp to plane end-grain surfaces to a high standard.
1 As opposed to the the more common type of mitre, the frame mitre as used in face frames on cabinets or picture/mirror frames.
2 Something like the same setup could be arranged for hand sanding too, but you'd really only want to use this for finalising the angled face that you've produced by some other method or combination of methods, rather than creating it from scratch as you might on a power sander.
3 The edge of plywood is a mixture of long grain and end grain due to each ply being oriented 90° to the next.
4 If secondhand tools are available where you are I would suggest a vintage plane is a better investment, even if the cost is a little higher, but in some places older planes are available for much less than a budget modern plane while being nearly always of far higher quality.