Hypothetically, equally intellectual organisms are living on a near planet when and how would humans discover?

Hypothetically, we are living in an infinite universe. How far is a “near planet?”
If the planet is within a very close 200–300 light years, then there might be some possibility, within 200–300 years, that we might detect each other. If the life form is on the other side of the Milky-way, or in another galaxy, then there is no possibility.

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