The NGFMC does know the runway length, and if the field limit weight from the entered takeoff data exceeds the runway distance available, the FMC scratchpad message V-SPEEDS UNAVAILABLE displays. With this in mind, enter Flaps 10 or 20, and select TO 2. If no scratchpad message, then TO 2 is a valid rated thrust selection. An assumed temperature can then be entered. The FMC allows up to 25% off the selected rated thrust. The temperature that corresponds to 25% can be determined by entering a high temperature, 90 for example. The FMC will round the temperature to 25%, usually around 64C. Again if no message, it’s a valid performance solution. If the message appears, then try a lower temperature. The thrust break temperature is usually around 30C for a standard day. Enter values between 30 and 64 until the highest temperature value that doesn’t generate the scratchpad message is found. You now have the lowest thrust available for the selected runway.
If TO2 fails to give a solution, try TO1, then TO.
These are balanced v-speeds of course, and the FMC runway length may not be equal to the ASDA, TORA, or TODA distances. Again this is only a valid field limit weight. Obstacle limit, climb limit, Vmbe limit etc are not known.