There is no problem to reach a big pressure by itself.
There is problem to reach it for this amount of fuel using the same amount of fuel as energy source. The flow is fixed, so pressure is proportional to pump power, which is a part of turbine power, which takes energy from that fixed flow. To get more energy, bigger temperatures are needed - on both fuel-rich and oxidizer-rich turbines, and that's limited by existing materials.
Of course, there are many complexities with efficiencies, balances (spinning, two turbopumps), thermal expansions and contractions (LOX is about 90K), cooling of turbine blades, if any, control of pressure feedbacks (e.g. the bigger power on turbine - the bigger pressure on pumps, which supplies fuel to gas generator and then to turbine, so we have a positive reinforcement loop here)... No, the problem isn't the pressure - it's the pressure given all the constraints of the leading edge rocket engine.
Ok, but that still doesn't answer my question of what specifically SpaceX did differently. For instance, you said bigger temperatures are needed and that is limited by existing materials. So did SpaceX invent materials that could stand a higher temperature?
SpaceX has the first flight tested, full flow dual turbopump engine.
As in there are turbopumps for both the lox and methane tanks powered by burning extra rich mixtures for each pump leaving enough unburnt lox and methane in the perfect ratio to generate the record primary thrust.
