Why does the 737NG EGT drop during take-off?
Above is takeoff engine data$^1$ and is indicative of the behavior you've mentioned. (FF is fuel flow and TLA is thrust lever angle.) The same behavior can be seen here as well:


A 737-800 takeoff video
An "EICAS cam" video for what I think is a 777
An Embraer E190-E2 video


(The exact timing may depend on how long the engines are left in the stabilization process.)

Note: The 737NG EGT sensors are at the T495 station in the low pressure turbine section. There are 9 thermocouple probes and their average is displayed.

The CFM56 employs variable stator vanes (VSV) in the compressor. In general those vanes close at low engine speed and open at high engine speed (shown below).


  
  Source: CFM56-5A manual


The specifics are proprietary, but plausible conclusions can be made. When the engines are stabilized for TO/GA, it could be the ECU (electronic control unit) opening the VSV to provide the ideal compressed air for faster engine acceleration (more air before the fuel would lower the EGT).

Note: The VSV is controlled by the hydromechanical unit (HMU), which receives input (torque motor current) from the ECU (CFM presentation, PDF page 16).



Of course if you have cause for concern, don't use the internet for flight, and check with your airline.

$^1$ Lion Air Max crash report (sadly the only public source of FDR data I can think of is accident reports).