There is a frequently taught "rule" that sentences should not start with any of the coordinating conjunctions, i.e. and, or, but, yet, so, for, and nor. There is no actual grammatical rule as such, however, simply because such a rule doesn't make any sense. In fact, even the most ardent prescriptivists are likely to agree that starting a sentence with a coordinating conjunction is perfectly fine.
However, there is a reason that this so-called rule is taught. The goal is to avoid sentence fragments such as:
*He went to the store. And bought milk.
It is much easier to forbid starting sentences with a coordinating conjunction than to explain exactly how sentence fragments work, and this is how this "rule" came about. A perfectly fine sentence that does begin with a coordinating conjunction is, for example,
He went to the store. And having seen the milk, he bought it.
The word because is liable to similar errors; for example,
*He went to the store. Because he was hungry.
Like the coordinating conjunctions, it is perfectly fine to begin sentences with because, so long as you keep in mind that the goal is to avoid fragments. For example, the following sentence is perfectly acceptable.
Because he was hungry, he went to the store.
In American English, we don't normally write dates that way, but instead write and say with the month first — even if it's written day first, we'd still usually pronounce it month first. So "27 July" becomes "July twenty-seventh".
I believe other dialects usually, but not always, include the article before the day when putting the day before the month, so "[the] twenty-seventh [of] July". It will be understandable no matter which way you say it, but it's safer to use the slightly longer form to avoid sounding awkward in places that aren't that terse.
Best Answer
Just add a was or is after the date. Practically speaking, it doesn't really matter which one you use. Either one will work equally fine:
The sentence would actually sound a lot smoother if you rewrite it like this:
You can make it even shorter:
Or shorter still with the day I met you as a parenthetical statement: