Your belief that teeth can 'regrow' isn't exactly right, but that said, the old and firmly established idea that cavities cannot heal themselves or be reversed has been proved to be erroneous, with the caveat that, if the decay is severe and the tooth is painful, particularly if the root is affected, its a trip to the dentist before you get an abcess. In those circumstances, its unfortunately already too late for your tooth to heal itself.
However, research in the last few years does indicate that small cavities in teeth do heal themselves, given the right conditions, and in the UK and parts of Europe for the last decade or so, small cavities are left by the dentist to see if they heal themselves with improved dental hygiene. I know that they can do, having had personal experience of this with a younger relative.
A change in diet might be necessary depending on what you currently consume, and there's some interesting information in the link below, garnered from various scientific sources, including The Lancet (a well respected British medical publication). Having read it myself, I'm off to do further research, given I eat whole oats daily, and am also currently looking at the role of proteolytic enzymes regarding tooth decay and other health issues, another area of interest. I've not provided a link to the enzyme situation because I'm still researching it.
Whilst this answer does answer your question, any solutions are not 'fast' - and whether any of this actually counts as a Hack, I can't quite decide.
I have found the British Medical Journal report, also published in the Dental Association's Journal in the UK, and the link is below - however, if you want to access it properly, you have to pay, and I ain't that desperate to prove this information accurate!