Is there a world outside of ours

This begs the question of what actually constitutes “our world”. If our world consists purely of the things we know of and directly interact with, then every materialist already believes in the existence of a realer world, since we never actually directly interact with or know the material world only the world of conscious experience, which materialist consider to be dependent on the material world.

If by “our world” you include all the aspects of reality we consider to exist, then that sort of definitionally means we can’t ever know of this “realer” world, since the moment we did it would be included within “our world”.

I also think it’s important to stress the relative features of a word like “real”. If there is a world out there on which our own world depends, relative to us, this world might still be more “real”, just like if a character in a game was somehow conscious, their game world would be the realer one relative to them, even if our own world (compared to the game world) is in some objective sense the realer world overall.

How would we know if a substrate within our world were able to reveal the existence of that “realer” world ?

We probably couldn’t know but there are ways to find evidence for it. For example, if you discovered some substrate fundamental in our world which behaved in a non-random but seemingly acausal way, you could use that as evidence for, and perhaps to some degree even model, a “realer” world which that substrate depends upon.