The argument as you have presented it is capable of two interpretations. The first and more persuasive is that the evidence of God would necessarily be manifest by virtue of the fact that he tinkers with the world. In other words, evidence of his existence would become manifest despite God’s best attempts to cover it up.
The second suggests that God would have an interest in unmistakeably revealing himself. It is less persuasive because it assumes the knowability of God’s motives.
Turning to the first interpretation:
In dealing with non-sentient phenomena, one is entitled to judge the reality of the phenomenon under question by reference to the extent to which it would be likely to manifest itself compared with the extent to which it does manifest itself.
Thus, if, as advertised, psychic powers belonged to us all but only some people seem to have mastered them, one could argue that given the evident usefulness of psychic powers and the evolutionary advantage they would give, one should expect to see vastly more unmistakable examples of it. Footballer kickers who had telekinetic powers should self-select as being able to make the ball go further and more accurately in a way that would result in two populations of kickers being apparent - those with telekinetic powers and those without. Yet notwithstanding that there are good and bad kickers, they still all seem to come from the one population “talent” curve.
Indeed, psychic powers should be a well-understood part of everyday life, not an elusive phenomenon only “detectable” at the very boundary of detectability, and generally within the error limits of the detecting systems. If they were true. And this is a good argument for their non-existence.
Similar arguments can be made for intelligent creatures, but they are subject to the observation that intelligent creatures can make a choice to avoid being seen. One can imagine some sort of “prime directive” that would mean that aliens from other planets might not wish to be seen. Nevertheless, assuming for the moment the existence of little green visitors, we can infer that their capacity to hide is not perfect, otherwise there would be no claims of sightings at all. And there are no secondary phenomena - fragments of space ships, alien corpses, etc. Once again, there are just purported dubious observations at the limits of detectability, when if people were being abducted as frequently as claimed, even covertly, one would expect to see something much clearer. After all, all criminals do their best not to be detected, yet they typically fail in the endeavour.
The atheists’ argument is like that. Even if God does not want to interfere too obviously, he can’t tinker with the rules of physics too often (by performing miracles) without it leaving unmistakeable traces. The assumed existence of miracles at all disproves the idea of a clockmaker God who simply set the world in motion and left it to its own devices. And the rate of miracles claimed by various of the televangelist persuasion indicates a huge rate of tinkering. So you would expect to see secondary phenomena.
The response of theists is, of course, “Look around. The evidence is there for anyone to see. The beauty and majesty of the world . . . blah de blah de blah.”