This is a copy of my contribution to a discussion some time ago about bleeding brakes and being unable to gain any pressure.
Given that the hoses are not ruptured, in my experience lack of lever pressure tends to be a result of pushing against air which compresses and absorbs the pressure so that when you release the lever it expands and prevents new fluid entering the system;
pushing against something like a piston seal or dust seal which has stuck through damage or dirt and is not allowing the piston to slide forward fully against the brake pad - again on release of the lever the piston moves back by the torsion force of the seal rubber maintaining the feeling of sponginess in the system;
or, not pushing at all because the master cylinder seal is allowing fluid to leak around it because it it worn or ruptured.
Given that you say that you do eventually feel pressure, my money would not be on the master cylinder being at fault. The little squirt of fluid as the master cylinder piston passes the reservoir hole is normal - don’t squeeze too fast when the reservoir lid is off! It also indicates that the piston is pushing fluid as required.
In older systems it is fairly common for the shiny sliding surface of the calliper pistons to become corroded as they gradually creep out and are exposed as the pads wear. Along comes the mechanic who, charged with replacing the pads against a time schedule, pushes them back in, introducing the roughened/dirty/corroded piston sliding surfaces to the rubber dust and pressure seals. The result - jammed pistons.
Newer systems seem to have pistons made of synthetic material that doesn’t corrode, but the same problem can occur if not cleaned properly before pushing them back when replacing pads. Remember, where the pistons work is a hostile environment contaminated with brake dust, road grit, rain, salt etc.
I clean my calipers each time I replace my tyres, using brake cleaner and an old tooth brush and wiping the dust seals with red rubber grease on a q-tip. The result is pistons that can be pushed home easily with thumb pressure. Also, my understanding of the system is that the fluid in the hoses moves easily without obstruction back into the reservoir when the pistons are pressed home. This has to be the case to prevent hydraulic lock when the lever is released.
your situation sounds like either air in the system or the master cylinder seals having failed resulting in the piston not producing pressure.
There is no need to bleed the front brakes in order to bleed the rear brakes.
Alan R