If there was a Counter-Earth on the other side of the Sun, when would it have been discovered?

We are in a alternate timeline where there is a Counter-Earth that always stays perfectly on the exact opposite side of the Sun from our Earth. It has about the same size and mass as our planet, but is lifeless. It doesn't have a moon.

Everything that happened on our planet historically goes down the same way, i.e. the effective point of departure from our timeline is the discovery of Counter-Earth.

Roughly in what year would scholars first start suspecting Counter-Earth exists? When would its existence be proven? What tools would be used to do so?

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If there was a Counter-Earth on the other side of the Sun, when would it have been discovered?

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