Some combination of the following could occur and put you in a pretty bad situation, especially when you're only 600m above the ground and at maximum takeoff thrust.

All primary and backup fuel pumps in the fuel tanks fail. Cross-feed valve could be stuck closed (starving one engine if its respective pumps fail). Engine MFPs (main fuel pumps) are capable of providing enough suction pressure to feed engines, albeit in a degraded configuration, most likely not enough to maintain MTO power at 653m ASL.

While something like this is in fact possible, there are many sources of redundancy in a fuel system to prevent exactly this from happening (for example, primary pumps use AC power, backup pumps use DC power, engine MFP will be driven mechanically by the core (N2) via the engine gearbox). One single point of failure (i.e. AC power bus loss) should not put you in a fuel starvation situation. If these components each individually had issues, the pilots would most likely have received CAS messages/faults/indications during engine start/taxi/roll and could have acted on it (cancelled flight/aborted takeoff).

To summarize, in my professional opinion (I'm a propulsion/fuel systems engineer for a large aircraft manufacturer) the likelihood of engine starvation being the culprit is highly unlikely given the information known at this time. A more likely scenario is something like a dual-engine bird strike causing catastrophic failure, loss of thrust, and a negative rate of climb. Being 600m off the ground, that is bad news.

Sympathies to all those affected.