I very much doubt that any government would allow that, for obvious reasons.

There are other somewhat similar cases however.

In Finland, conscription may be avoided by being a Jehova's witness, that sole religion, on the basis of that it is a non-violent religion, ignoring that many other religions have similar tenants, and many non-religious people are also deeply pacifist who are still conscript. — That sole religion, so named, is exempted from conscription.

And one only need prove membership, not prove that one actually holds those non-violent beliefs to be exempt.

It's unfortunate that one needs to make up a god to be exempt from the some of the most awful governmental abuses like conscription, but I'd rather have such an exemption than not have it at all.