Wait for half a minute after connecting and before starting the engine and it'll work just fine. Not all current has to come from the jump starter. The jump starter can rapidly charge the car battery, and then the jump starter and car battery work together to provide the needed cranking amps. But before doing so, please be certain that your car battery is working and just flat, instead of being faulty.
The problem with jump starting cars having faulty batteries is that the jump starter or the donor car battery provides enough buffer for the electrical system. Once you disconnect, the only buffer is the faulty battery in the recipient car. If it's faulty, it can't act as a good enough buffer, meaning you will have voltage spikes after disconnecting the donor car or jump starter, and those voltage spikes can do expensive damage to car electronics.
If the battery is flat, it can't operate the starter motor. By once you connect the jump starter, it rapidly charges the battery. If you charge the battery in 30 seconds and then for 3 seconds operate the starter motor, it essentially multiplies your current by 10. The 400 amp jump starter would effectively work as a 4000 amp jump starter (except the car battery can only give 850 amps, limiting the performance).
Actually, if you don't know if the battery is only flat or faulty, it might be a good idea to charge it for a few minutes with the jump starter, remove the jump starter, and try starting the engine on its own. That eliminates any chance that a faulty battery could be too little buffer for the electrical system, causing expensive damage from voltage spikes.
Also the 850 amperes of the battery are probably needed only during very cold days. If the day is not that cold, the 400 amperes might be enough without needing any more amperes from the flat battery.