Cold viruses are not retroviruses and cold viruses do not integrate genetic material in to their host's chromosomes.
So we'll strike "cold" virus from the original sentence and insert "retro virus". Like this:
God did not "design" retro virus DNA into human/primate DNA. Viruses do that on their own. Every time you get a [retro virus] is proof that they do.
Now it's your turn to show evidence that God "designed" broken retro virus DNA into primate and human DNA in a way that looks identical to a common ancestor, just to fool us.
Then you need to get your concept through Occam's razor as to why it's a better explanation that an unseen, unmeasureable, intellegence is messing with us via retrovirus DNA rather than it was just a simple infection in a common ancestor millions of years ago.