No.
The first distributions from your 403(b) for the year are your RMD from the 403(b) and RMDs are not eligible for rollover. You can only roll over money from the 403(b) to the IRA after you have satisfied the RMD for the 403(k). You can then make a QCD from the IRA, but it will be a distribution in addition to your 403(b) RMD for the year.
After receiving this year's RMD from the 403(b) and rolling over the entire remaining balance to a IRA, you'll be able to make QCDs next year and beyond that satisfy your RMDs for the IRA for next year any beyond, but not for this year (and you won't have any RMDs for the 403(b) for next year and beyond because the 403(b) will no longer exist).