Hi Julio,
The fact that your site is 'just' missing H1s and likely only using H2 shouldn't be too big of an issue. I'd say that Google is smart enough to notice that you basically would use the H2 instead of the H1 everywhere. However, I would make sure that the use of the H2 is not overdoing it. If you have 6171 H2s on your page then obviously its value is minimal. It's in the end, all about the proper use of these tags, and in that case, it shouldn't matter if there is no use of the H1 tag.
Martijn.