If this is a new employer, then no, you cannot deduct the temporary living expenses.  Your new work location is considered your tax home.  Generally, you cannot deduct expenses from your tax home.  Your tax home is where you work, not where you live.

When an employer sends an employee on a temporary work assignment, which is outside the commuting distance from their home, then temporary living expenses may be deductible.  The temporary assignment is one year or less.  Any time greater than one year is considered permanent.

If you will be in this new work location permanently, then you can deduct moving expenses that were not reimbursed by your employer.

See this TurboTax article What is a Tax Home? for more information.