RAW is NO, but their intent may have been YES.
How is that for confusing? Stay with me,there is a great moral at the end of this, too!
Starting with the RAW
Adam's answer covers the DMG (pp 252) for Adjudicating Reaction Timings and comparing the wording of Sentinel against Shield and Counterspell which together are an excellent argument for the Sentinel attack occurring after the enemy attack has been resolved (hit or miss).
Jeremy Crawford also confirms this in his Sage Advice Tweets.
Despite the desire to have Sentinel preempt an attack, that's not how the feat is written. A DM can override that.
By default, a reaction occurs after its trigger. Opportunity attacks and the shield spell are example exceptions.
Intent was possibly, maybe, could have been Yes. By at least one of the devs.
However, the conversation with the developers didn't start with Crawford, it began with Mike Mearls. And he, not being the official Sage Advisor, does not give rulings, but talks about he generally plays it or intended it. What he said was:
I'd say it's before - it's similar to an opportunity attack; that triggers before the creature leaves your reach
sentinel's design intent is to protect other PCs, so in that case should be before
Concept vs RAW
This is an excellent example of the intent vs the rules conundrum. Intent can mean the developers beliefs in how the ability works OR the Player's vision of what their character is doing. And when the rules aren't explicit (although beware of adding benefits just because the rule doesn't prohibit them) about when the attack occurs, that interpretation becomes more valid.
Jeremy Crawford ended his remarks with something we often forgot - and we should remember this:
To be clear, Twitter is a way to be in touch with you, our fellow players and DMs. The upcoming FAQ is official.