How about trading pick 3 to Atlanta in exchange for pick 8, their 2nd rounder and Kyle Pitts?
Atlanta gets to take Jayden Daniels, NE picks up an extra second and a starter at TE. They take a LT at 8, then can target an RT and a high end WR2 with their two 2nds. They can send their 3rd or 4th to Chicago for Fields. Sign a WR1 in free agency.
Now you have QB, TE, LT, RT, WR1 and WR2 addressed and still have cap room left to make some other signings, and can go Best Player Available with your 4th rounder onward.