APOG: Why do you assume that God, if he does exist, wants us to know he exists?
It is a natural question that emerges from institutional religion.
The Christian God (Islam and Jews also) supposedly wrote books or inspired men to proclaim revealed "truth".
The DNA idea is an example of the minimum a god might want to do and it would have been more convincing than so called pronouncements from human intermediaries.
Of course there is so much more that a loving god might do to make his "children" secure. Frequent open forums with regular visits by actual materialized angels might be one. You could list thousands of things an almighty being could do that would persuade humans to carry out justice.