Since even NASA admitted they cannot travel past low earth orbit, how can we believe that there is even an Outer Space instead of a Dome?

Your belief is neither required nor relevant. The proof exists regardless, and it is vast and readily available. 

Perhaps a brief course on modern Astronomy or Cosmology would enlighten your view. 

This post was edited by Don Barzini at November 6, 2019 5:23 PM MST

There's a dome and it's the egg's fault.  I saw that Stephen King movie as well 

Define low earth orbit. When did you become a scientologist?

Well then how did the Reflective Mirror get on the moon? The astronauts  placed a highly reflective mirror on the moon and scientist on earth still use it to figure things out by shooting a laser beam at it (I think it helps them figure out distances of other galaxies and stuff like that). Cheers!

I doubt NASA "admitted" any such thing.

https://stuffin.space/

"Low Earth Orbit" wouldn't include Mars ... and we've sent numerous probes there.
Not to mention all the probes we have sent within our solar system.
Nor Voyager 2, which left our solar system.

Whoever actually "admitted" it, I'd be very surprised if it was NASA, unless talking about something very specific not mentioned above!

Forty-two years old, still in active service without maintenance, and still sending back information... Voyager Two, now following her Voyager One sister on their solo ways into inter-stellar space within the Milky Way, rather than as "just" passengers with the Solar System.

I find it an impressive feat, and rather moving. A wonderful tribute to the scientists and engineers who designed and built these two probes and their launching-rockets, and navigated and tracked them across and out of the Solar System.

Apparently this is the complete statement by NASA:

NASA says that we simply cannot go any further than low Earth orbit, with currently in service manned spacecraft.

And it would seem that statement was made by NASA about 18 months ago.

(Since this is apparently old news, finding the context of the quote requires more time than I am willing to invest at the moment.)

Since the conclusion of the Apollo program, NASA has not built a manned spacecraft capable of escape velocity. With CURRENTLY AVAILABLE MANNED SPACECRAFT they can't go beyond LEO. Juno is currently orbiting Jupiter, Cassini dived into Saturn not long ago and China currently has a robotic rover on the Moon.

AH-HAH!.

Thank you Tom and Slatibartfast!

That clarifies it. The original quote missed that vital qualification!