I don't think your should modify your story just to make it "more sci-fi." Science fiction and fantasy are very broad categories, and I think your original premise fits.
Don't dilute the intent of your story just to fit a box. Let the readers decide. Consider Station Eleven, one of the recent Sword & Laser picks. It's a tale of a pandemic and life after that, not too far fetched. Write the story that will have the most impact and readers will enjoy.
So you’ve inadvertently trapped an ancient trans-dimensional god in your backyard shed; what do you do? That’s what Venus McKenzy and her friends would like to know.
1635: a war veteran, troubled by visions of the future, enters the Pantheon in Rome. He seeks answers. He needs redemption. A five year old girl, and her female-line descendants in the present day, hold the key to the future of humanity,
Great voice. I'll keep an eye on this one.