First of all, I think there are plenty of life forms in the Universe and probably in our Galaxy as well. But life doesn't mean to be intelligent, it can be just wild animals and plants on a random planet.

Just think, what allowed hominids to evolve and become what we are now? Just a random thing - asteroid have killed big predators and cleared all the way for small mammals. What I'm talking about is life shouldn't necessarily be intelligent, contrary it has a very low chance for it.

Then, if we have a few luckers in the Universe to achieve the level of life form that at least allows to ask questions like we do in this thread, they have to exist at relatively same time and close to each other so they could have a possibility to contact. Is this real? In theory, yes. But practically it lowers chances (again) too hard that it might be an extremely rare thing in all universe.

And the last thing is interstellar traveling. We should turn to relativity theory again. We can't reach far distances now and we won't in the future just because speed of light is our limit. Warp drives, wormholes, quantum teleportations etc still stay fiction and there is no guarantee scientific progress no matter how high it is may open interstellar travels for us even in the far-far future.

That's why I think alien contacts are rare in the Universe, but primitive (simple animals, microorganisms, plants) or isolated life forms might be pretty common. Maybe we even can't imagine how it's common.

TL;DR: Intelligent alien contact might happen if:

1. Life has to be born on a planet with required conditions.
2. It has to reach a high level of intelligence.
3. At least one another intelligent alien civilization should also exist in closest distance.
4. Both should appear relatively at very same time .
5. At least one of them should have technological advances to reach closest planets and stars or opportunity to send the message.