No, unfortunately, since you didn't reside in the home for any of the 5 years, you can't meet the test of residing in the home for a total of 2 of the last 5 years before the sale to qualify for the exclusion.
You are correct in that there can be relief for taxpayers who moved for work, but again, you would have to meet the residence test.
Here is a more easy-to read summary that explains Publication 523: Tax Aspects of Home Ownership: Selling a Home
