Does anything have inherent meaning, or is meaning only a product of the mind?
There seems to me to be a fundamental ambiguity there.
'Meaning' as in how the word 'dog' (the sound or the ink squiggle) means dog (the animal species)? In this case, what a word means is what it refers to, its referent. (Which may be concrete, abstract or even fictional as in 'Sherlock Holmes'). That's basically arbitrary since different languages associate the same things with different sounds and squiggles.
Or 'meaning' as in how a beautiful sunset or a beautiful flower inspires a feeling of the sublime? I think that's a psychological response, with a big emotional/affective component that isn't necessarily present in the word-meaning case. Whether it's learned or inherent in human beings is an open question. But I do think that the beauty of a flower, let alone any meaning the flower might have, is something that comes from us and isn't inherent in the flower.
https://en.wikipedia.org/wiki/Sublime_(philosophy)
So there's a word-meaning sense of 'meaning' and a less well defined life-orientation sense. In the latter case, something is 'meaningful to us' if it helps us orient ourselves in our lives. The meaningful thing might inspire us somehow, or remind us of something that we find emotionally resonant.
'God' might be literally meaningless in the semantic word-meaning sense since it (arguably) doesn't refer to anything real. (Even though it arguably does have a fictional referent. Speaking meaningfully about non-existent objects is one of philosophy's open problems.)
But 'God' might be far less problematically meaningful in the second life-orientation sense since faith in God structures how many people think of the universe and their own presence in it. In that sense it would seem to be meaningful in much the same way that 'beautiful' and 'good' are.
There are other sorts of cases that philosophers discuss.
Does smoke mean the presence of fire? Not in the word meaning sense, though it is indeed a sign of fire. The connection there seems to be causal but probabilistic, since smoke might sometimes have a different origin. But having said that, in order for smoke to be a sign of fire, organisms have to recognize smoke as a sign of fire, so there's an interpretive mental component too.
https://plato.stanford.edu/entries/peirce-semiotics/
Science is founded upon relationships like this. Which suggests that people who think scientifically (scientistically?) will want to reduce the other meanings of 'meaning' to the causal examples somehow. A great deal of philosophy of mind and neuroscience seems to be devoted to that in one way or another.