No, the IRS expects you to report the gains/losses in the year they occurred. Your brokerage will report this to the IRS in the proper year, so you'd have issues from the jump if you tried to claim the gains for the prior year.
Note that the $39,375 threshold for the 0% long-term capital gain rate is based on taxable income (AGI - deductions), so you can still be in the 0% long-term bracket above $39,375 gross income.