Jim Hardy has the most passing touchdowns in a season in his first 4 games, with 10 touchdowns in 1950.

who has the most passing touchdowns through the first 4 games of a season
1950Hardy1950Thompson1953Enke1950Albert1950Baugh1950Gilmer1950Layne1950Van Brocklin1950Graham1950Christman1950Conerly1950Geri1950Waterfield1950Mackrides1950Gage1950Luckman10764444442222211
NAMESEASONTMGPTDCMPATTPCTYDSAVGYDS/GTD%INTINT%SCKSCKYRATE
Jim HardyJim Hardy1950CHCCHC4103911334.56695.9167.38.81311.545.4
Tommy ThompsonTommy Thompson1950PHIPHI47328040.04916.1122.88.878.853.7
Fred EnkeFred Enke1953BALBAL464710445.26626.4165.55.887.753.4
Frankie AlbertFrankie Albert1950SFSF444810346.65215.1130.33.965.850.7
Sammy BaughSammy Baugh1950WASWAS34325756.14307.5143.37.023.589.1
Harry GilmerHarry Gilmer1950WASWAS44195236.54168.0104.07.747.759.5
Bobby LayneBobby Layne1950DETDET444510443.36336.1158.33.854.856.3
Norm Van BrocklinNorm Van Brocklin1950LALA44428450.06587.8164.54.856.067.5
Otto GrahamOtto Graham1950CLECLE445410850.07256.7181.33.798.349.3
Paul ChristmanPaul Christman1950GBGB3262227.3813.727.09.114.553.8
Charlie ConerlyCharlie Conerly1950NYGNYG42195832.83185.579.53.423.449.4
Joe GeriJoe Geri1950PITPIT42142751.92188.154.57.427.472.8
Bob WaterfieldBob Waterfield1950LALA42336451.64066.3101.53.134.762.4
Bill MackridesBill Mackrides1950PHIPHI3292536.01716.857.08.028.053.9
Bobby GageBobby Gage1950PITPIT31123040.01565.252.03.300.068.2
Sid LuckmanSid Luckman1950CHBCHB3161442.91097.836.37.100.094.0
StatMuse has game-level data for passing touchdowns going back to the 1950 season.