Your question does not appear to be carefully stated which makes me wonder how much you are interested in an answer. However from your other posts on this forum I gather that you are trying to think about fundamental problems, but without any serious training or study. It appears you have thought about what was before the big bang, what is outside of the universe, and now, what might exist outside of or perhaps in addition to the commonly observed three dimensions of space and one of time.
In general, you seem to be asking, what can we know about that which cannot be observed? This question can be reduced to triviality. What can we know about that which we cannot know about? The answer is, nothing, or, alternately, everything, which is to say that the only thing we can know about it is that we cannot know about it, which we know, so we know already everything about it which can be known, even without speculation or observation.
Please notice that there is a difference between questioning what cannot be known and questioning what we do not know. There are many good questions about what we do not know, but only one good question about what we cannot know. What can not be known? Or, by negation, what can be known? Hence, by generalization, what is knowledge?
However, I was speculating along the lines of your dimensional question myself in a recent idle moment. I can't answer your question directly (it is a kind of question you can only answer for yourself) but maybe we can find a better question.
First, what is a dimension? Something which can be measured. Right off the bat, dimensions that cannot be measured are eliminated from the discussion. We will not spend our limited and valuable thinking time wondering about God's hat size. However this still leaves an interesting question, which is, are there dimensions which could be measured, but which we do not measure?
The answer is clearly yes, there are an unlimited number of dimensions we do not measure, either because our equipment isn't good enough, or because we just aren't interested because the answer is trivial.
For example, think of a picture frame. Maybe you have an 8x10 picture and so you want an 8x10 picture frame. 8x10 means you are interested in two dimensions, which happen to be, how long the frame is, and how wide the frame is. You are not very interested in the diagonal measure of the frame, partly because there are a lot of length and width combinations that could give you any specified diagonal, and partly because there is only one diagonal for any specified length and width. By giving the length and width, you also are giving the diagonal, but by giving the diagonal, you are not giving the length and width. It is necessary and sufficient to give length and width, superfluous to give the diagonal.
All physical objects have an infinite number of possible dimensions to measure. The real question is, not how many dimensions does an object have, but how many dimensions are necessary to completely specify an object as to shape and size? We have known for a few thousand years now that any physical object can be specified as to shape and size in three dimensions of space. You could measure more, but you don't have to, just as you don't have to measure the diagonal of a picture frame.
Physicists have one other dimension to measure, one which is not specified in the three spatial dimensions, and that is the dimension of time. How long does an object last? How does an object change? As far as we can tell, there is only one dimension of time, which has a past and a future and a present, that is that. All the concerns of classical physics are sufficiently described by these four dimensions, three of space and one of time.
Are there other dimensions? Of course there are, an infinite number of them. Better question: are there other dimensions which are necessary to describe the existence and behavior of physical objects? In other words, are three dimensions of space and one of time sufficient to describe every observable? The answer is, probably not.
We have a variety of evidence for this conclusion. The evidence is based on observations, measurements, of physical objects in three dimensions of space and one of time. We have not been able to explain, using three dimensions of space and one of time, all of the behaviors of physical objects which we have observed.
It turns out that it is easy to describe an object (and after this I will include the behavior of an object as part of its description in four dimensions) in more than four dimensions. Sometimes you may need to do so. You may want a blue picture frame. But there is a difference here. It may be that if it is not exactly the shade of blue you desire, it will still work. But if it is not exactly 8x10, it will not work. The color may be important, but it is secondary. If you are still in doubt about this, think about it this way: if there is a picture frame available in the exact color of blue you want, but it is a 22x30 instead of an 8x10, will you buy it and be satisfied? Probably not. You will first consider the size, and only if the size is correct will you go on, second, to choose the color. The color may be important to you but it is secondary to the size.
There are three regions of our observable universe of which I am aware in which material objects do not seem to be suffiently described in only four dimensions. These regions are the very large, the very small, and the very dense. One could add others, such as the very vacuuous, or the very long in time, or the very short in time, but we can only imagine these regions, and do not have any way of observing them at present. I am therefore aware that they may exist, but in no way aware that they do exist, even though I believe they do exist.
The very large is studied in cosmology, the very small in quantum theory, and the very dense in condensed matter physics.
In cosmology, there are conflicting observations which seem to suggest that something is going on outside of the four classical dimensions. The universe is not expanding at a reasonable rate. Galaxies are not rotating at a reasonable rate. And we cannot explain why the universe is so self-similar to the left and the right, up and down, foreward and backward. These problems are known respectively as the dark matter problem, the dark energy problem, and the horizon problem.
The very small is the realm of quantum physics. Very small objects do not behave reasonably in four dimensions either. They may appear to be in two places at one time. They may appear out of nothing and nowhere, and return to nothing and noplace without any warning or consequence. We have no reasonable explanation of observed mass and charge. We do not know why the force of gravity is so much weaker than the other forces. Some of these problems are discussed under the topics of wave-particle duality, quantum entanglement, virtual particles, and of course, string theory.
Then in condensed matter physics there is the problem of singularities, such as black holes and the big bang.
I don't mean to suggest that this is a comprehensive or exhaustive list of questions. There is a lot of crossover, and too much unexplored territory. But if you have followed this discussion, you may now be in a position to rephrase you question about the existence of beings in other dimensions.
My idle speculation, which is what caused me to answer this post, is as follows. Every physical object exists in all four dimensions. We do not see any object that has zero dimension in width, height, length, or duration. Of course, we may only be interested in one or two or three of the four dimensions and ignore the presence of the others, but in no case is there any tangible object which lacks existence in any of the four common dimensions.
We should be able to extend this logic to higher dimensions. If the higher dimensions are fundamental, and therefore necessary to the description of an object, then any and all observable objects must have measurable existence in that higher dimension. So, if there are higher dimensional beings, their being must be expressed in all four of our common dimensions, ruling out the possibility of beings which can enter or leave our universe by means of their higher dimensional will. No god can put a finger in and stir things up and then leave again to some undetectable dimension.
There is still one area which I have not discussed directly in this post, and that is the possibility inherent in space-time equivalence that there are other directions, or dimensions, in time, than the one with which we are so comfortable. My idle speculation above includes these possible other directions in time. If they exist, we should be able to measure them in every observable object. They should have an effect on our common dimensions. And I believe they do. My study has been toward a reasonable demonstration of this effect, but it is not complete. And I may be wrong. It is my goal to put this question forward in a manner which is stated clearly enough to be falsifiable.
Thanks to our mentors on Physics Forum for space and time to consider these matters in public.
Richard T. Harbaugh,
Nightcleaner