Typically when the brakes respond to “pumping up” it means either air in hydraulic system or an adjustment issue.
Quick checks to try include taking 4 pairs of vice grips and clamping off all 4 flex hoses as close to the frame end of the hose as possible. Try checking the brake pedal again. If it is now a hard pedal, take one pair of vice grips off at a time and check pedal again. Put vice grips back on and go to next caliper and repeat. You should be able to locate where the issue is. To check the flex hoses for “ballooning” move all 4 vice grips to caliper end of hoses, then go through the removing vice grips and testing procedure.
If the brake pedal is still soft with vice grips applied you very likely have air in system. Bleed brakes at the master cylinder first. If the master cylinder is mounted to brake booster at an angle remove master from car and bench bleed the master cylinder in a bench vice using two lines you either buy or make up yourself that simply loop from the master back into the resevoir. Using a push rod pump the master cylinder slowly and watch the ends of the two lines in the resevoir for bubbles. Keep pumping until bubbles stop. After bubbles stop, leave the lines connected and carefully re-install master cylinder. After master is mounted remove test lines and reinstall original lines to master. Leave lines slightly loose and have someone simply apply brakes. DO NOT PUMP THE PEDAL. Tighten both lines before releasing pedal. Release pedal and wait 10 seconds. Loosen both lines again and have brake pedal pushed down again. Tighten lines before pedal hits floor. After you stop seeing bubbles coming out the connection at the lines stop bleeding. Make sure that the resevoir never runs out of brake fluid.
A bad master cylinder will generally show itself by having the brake pedal slowly going to floor under very light pedal application. This generally happens at stop lights when you are pushing brakes hard enough to hold the car from creeping forward when stopped. A hard application of the brakes will usually give a hard pedal. The reason for this is due to the shape of the seals inside the master. They are cup shaped seals and the hydraulic pressure on a hard application of brakes uses the hydraulic pressure to drive the seals tightly to the bore increasing the quality of the hydraulic seal. Any fluid that leaks past those seals goes right back into the resevoir via the compensating port.