That sounds like a challenge, has anyone ever managed to do that or was that the challenge that resulted in the invention of guide bushes !!
I wouldn't suggest it if I thought it was particularly difficult.
I've made templates this way several times.
You can calculate and draw a circle diameter to make any finished hole size you want from any combination of cutter and guide bush you have that work together.
Use a 1/4" not 1/2" router. Mark with a 0.5mm tubular pencil.
Like a piece of woodwork decide to leave the line, or take the line.
Rough cut first and leave just a few mm inside the line then settle down and cut arcs sneaking up on the line then turning your workpiece so you are always holding the router in a position with good control, and cut another arc.
When you try it, you will discover why for shaving cuts that just remove a tiny amount of material, climb cutting with the router is a technique to learn, not something to dismiss just because it's not the conventional wisdom.
Big holes you can cut with a trammel bar, but 30-50mm handheld is the way.
And wear eye protection, you need to get close ish to the cutter to see clearly, but keep your face up and out of the line of fire. You are taking very fine cuts at the end so there is minimal stress on the cutter.
Let's say your template MDF is 10mm thick. Rout to the line but only 5mm deep.
If you mess up, you can flip the board and try again on the other side.
Pop a tiny hole through the board and draw matching circles on both top and bottom sides before starting to cut if you are worried about that.
When you have your good circle, use a flush bearing guided bit, top or bottom bearing, to flush trim the inside of the template to the 5mm deep section you've just completed.