You are assuming that all religions make claims that can be proven false, which is not true. Not all religions even have theistic beliefs.
As far as your later comment that if a God can make DNA, then why can't it do something less complicated like make us believe in it, there are a number of problems with this position: 1. You assume one God as opposed to many. 2. You assume this alleged God would want to make its presence known. 3. You assume that it would be easier for this alleged God to prove to us it exists than to make DNA. If we gave this alleged God a characteristic, like being "all powerful," then how could it ever prove to me that it is all-powerful? It couldn't. Even if this alleged God did every thing I asked of it for the last 20 years, for all anyone knows, the very next task I ask this God to perform, it won't be able to do. So, it would actually, depending on how one defines this alleged God, be far easier to make DNA than to prove it exists.