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According to the theory of general relativity 'space' can be bend like a fabric.

Objects with a lot of mass bend spacetime like a well or a bowling ball on a stretched blanket.

It (images) always look like spacetime is being 'pushed' downwards thus objects swirl around the more massive object (if their velocity is fast enough to not getting pulled into the singularity).

So I seriously ask myself, is it possible for objects / matter in the universe to push / bend spacetime 'upwards?'

Upwards in the sense that the ball in the picture (above) is bending spacetime in the other direction (vertical).

Though one problem arrises in my head already, wouldn't objects be invisible to our eyes since ,just like with the bowling ball and the blanket, it would be a layer under the actual play field <-- Instruments should be able to detect their impact right?

Info: I'm just a hobby astrophysics learner, not a physicist or a professional student in this field, so anything I've written down could be non-sense / false. Correct me if that's the case.

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You refer to "embedding diagrams" where the "squares" of space or spacetime retain their size, but buckle out into an "embedding dimension." Compare this to the 2-dimensional surface (not volume) of the Earth being embedded in a 3-dimensional space. There is no "up" or "down" in the embedding dimension.

An alternative approach to embedding diagram is to simply deform the "squares" of spacetime in place, in the two dimensions of a map rather than an Earth globe. Feynman has a lecture on a "hot plate" that demonstrates this approach. Kip Thorne also describes measuring rods that bend and stretch in his pop-science book "Black Holes and Time Warps."

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