Absolutely no need for engine to be running since system is hydraulic! But a running engine does make stopping the car a little easier on the road...
Did you bleed the calipers and flexible hoses before reconnecting them to hard lines (put end of flexible hose in cup of brake fluid, and apply vacuum at bleeder till fluid is flowing into catch container between vacuum pump and bleeder valve, then connect flexible hose to hard line)? Are the hard lines all new? There must be a huge volume of air in the system if you didn't, so what does the pedal feel like when you pump it (as previous poster says, try not to push pedal beyond normal range)?
I use a power bleeder similar to this
https://www.amazon.co.uk/dp/B000ROARTI/ ... T7FXNKWY47 which is a fantastic tool for efficient, one-man brake bleeding. With the amount of air you have in system it will be extra helpful. You don't even need to fill it but fill the reservoir, attach power bleeder and raise pressure to max 15psi. Then open a bleeder and wait for fluid to be pushed through. With the amount of air now in the system you may need to go round the car several times before all air is bled out, but this is no effort at all with a power bleeder. Get hold of the kind where you pump up pressure, not the kind pressurised by air in tyre as you have no control over the pressure, and the standard inflation pressure of a tyre is way higher than is safe to use on seals in master cylinder and servo.