Overall I think this is coming together. Good job!
I've made a few notes below, but I believe you're close with this one. Hope my comments help.
For most of his life, Alex was locked outside of time. The long years that crawled by inside the metal box, passed in the blink of an eye for the rest of the world. (I suggest reordering this sentence to something like: While time passed in the blink of an eye for the rest of the world, inside the metal box the long years crawled by for Alex.) When he finally escaped, broken and bloody, the only clue he had was the number '7' tattooed on his wrist. (outside of that one quibble, I like this opening. The only other suggestion I might make is to add what that clue lead him to do, at the end, but only if you can keep it short. eg. becoming a detective.)
Now, with the ghosts of his tortured past as company, Detective Alex Stokes investigates crimes involving the time-stopping technology known as Borrowed Time. All evidence of those responsible for his imprisonment has vanished without a trace, and Alex is left hoping that one of his cases will give him a lead that might get him back on their trail.
A new case involving a tragic bombing
justseems to be another dead end, until Alex makes a startling find - the attack was carried out using the same technology that trapped him for so many years. While the bombers have covered their tracks, and their motives remain unknown, the discovery of a young boy with the number '247' tattooed on his wrist may be the key to solving both cases. (I tried to sort out this paragraph, but I wasn't quite sure how to divide it. For transition, I believe it would flow better if the paragraph started with "when" (or something to show progression). And while I don't think that the content needs to be changed, I do feel like this could benefit from another period or two.)
As Alex gets closer to catching the bombers, his persistence makes him a target. If he wants to solve the mystery of the young boy, and get the answers he's been after, Alex will need to once again free himself from being locked outside of time. But this cage is more complete than the last - and that one took him 23 years to escape.
BORROWED TIME is speculative fiction aimed at a new-adult audience, complete at 130,000 words, and set in the near future.