Strong atheism makes the explicit claim that no gods exist and that there are ways or reasoning that support their contention.
Which God doesn't exist?
It is, in fact, a pretty tall order to absolutely prove that anything doesn't exist, and really dedicated strong atheists may be thin on the ground. But it really depends on the extent of the powers which are being claimed for the deity.
If a claim is being made about the deist god - who is claimed to have simply created the universe and then disappeared - then presenting absolute evidence for his non-existence is difficult. (However, the fact that absolute evidence for his non-existence is difficult to find does not make his existence likely.)
On the other hand, if it is claimed that the god in question, answers prayers, manages evolution, carries out miracles etc then it is possible to state that this god is extremely improbably as there is no evidence of these activities being carried out by a supernatural being.
In fact, the more that is claimed for any god the easier it is to demonstrate that it doesn't exist.
In this case absence of evidence is evidence of absence.
Furthermore, the less that is claimed for any god the less easy it is to disprove, but conversely the easier it is to ignore. This would seem to leave the theist with the impossible position of either trying to support an extremely improbable interventionist god or an utterly irrelevant deist one. Presumably, for those of faith, the challenge is getting the correct balance between impossibility and irrelevance.