One argument for God and creatures having being in common is
If there is nothing common to God and creation, we cannot know God by knowing creation.
But we can know God by knowing creation, therefore, etc.
The “we” in this argument is too vague: if the “we” were the persons of the trinity then then God can be known through creation as “what we caused ourselves”. So we have to give a more precise account of the knower as one who knows by abstraction. This gives us:
If being is not common to God and creation, then those who know by abstraction cannot know God.
We humans know God by abstraction, therefore, etc.
But this gives rise to a few objections:
1.) Being cannot be known by abstraction, since abstraction requires leaving something behind as not abstracted but our idea of being does not do this. Minimally, abstraction requires understanding one thing without the other, but being cannot be known in this way. What is common and peculiar do not differ as beings. This is why later Scholastics fell into talking about our idea of being as arising from an “imperfect abstraction”, though none of them knew quite what this was. And so it is far from clear that knowers-by-abstraction know being by abstraction at all, much less that they understand some feature in it common to God and creatures. This is not quibbling – it opens the possibility that there is some sort of at least implicit pre-abstractive knowledge, and many such accounts make some sort of reference to divine activity.
2.) If God is known by way of causal inference, then the argument requires that causes in themselves have something in common with their effects. But this is not the case with causes as such. If every causal account is explanatory, and no explanation presupposes what it tries to explain, then causes as such do not and cannot share some common feature with their effects. This is not a denial of the axiom nihil dat quod non habet, but only specifies that any common feature held between the cause and effect, if said of causes as such, is present only virtually or precisely as able-to-be-caused. This in no way requires some common field of action in the world. And so in order to understand God as the cause of the world, we must deny that there is something common to him and the world, not affirm it.