From an ATC perspective according what I saw so far .
The aircraft was on a flight plan but actually departed 1h late , this is not unusual , Tech problem was reported in another site , even that the tech problem was not (or could not be) fixed and a/c departed with item not signed, ( Twitter) , the flights plans are all passed to air defense / military, together with the transponder code the aircraft will have on departure.
Normal VHF contact with Khomeini TWR , normal departure, following SID with normal rate of climb for a 737 ( FR24) . transfer of control and frequency to Mehrabad APP/ACC ( located on the other Tehran airport in city ) positive contact . The Mehrabad centre is a joint cicil military unit using the same data processing system , so the flight was correlated and know to the military at the center on departure . . The aircraft was then cleared to climb to FL260 ( Iranian CAA) . 5 min after taking off . aircraft disappear from Radar ( Iranian CAA) would indicate Mehrabad APP/ACC worked on secondary only. Aircraft was called by ATC , no answer (Iranian CAA)
Now , If the aircraft Transponder was jammed by outside forces ( e.g. USA) the aircraft would indeed have disappeared from radar displays but then the VHF would have stilled worked, and the crew able to answer the controller calling them after the SSR loss.
If the VHF was jammed from outside( possible and relatively easy to do ) it would have affected everyone else on that frequency, but there is report that another aircraft on the frequency reported to ATC seeing an explosion ( Ukraine and Iranian CAA).
Therefore one can assume that the moment the transmissions stopped was the moment the first missile hit . Therefore the contents of the CVR/FDR will be of no real use as they most likely stopped at the same time .
The thing that is unclear to me , again from an ATC view, is that normally once an aircraft is positively correlated as civil one by the military system, this info is passed to air defense which automatically correlate the associated primary track on their system , and keeps this until it cross their State boundary if it is an international flight . Same for an incoming flight to the country.
Now, If we believe some twitter messages from Iran dissidents posted after the event, where it was suggested that a massive cyber attack was taking place on Iranian air defense communications that morning. That could perhaps explain why the data was not transmitted. But as this in unverified it is pure speculation from my side .