The https://en.wikipedia.org/wiki/Czochralski_method is the actual big crystal growing process, to which this quartz is just the input. Effectively we repeatedly make a crystal with the impurities moved to the end, then saw off the end and discard it, then re-melt the crystal to make it even purer.
It’s not the size that’s hard but the 99.9999% purity. The quartz from these mines is crushed, sorted for impurities, and fused/annealed into larger crystals before they’re ready for the semiconductor industry.
The single crystals of silicon that are made are cylinders with a diameter of 0.3 meter and a height probably of around 2 meter or even more.
The crucible must be bigger than that. The crucible is made from fused quartz glass. So the mine does not need to have big quartz crystals. They must be only pure. The mined crystals are melted together and processed like any glass, except that processing quartz glass is difficult, due to the very high melting point and the high viscosity of the melted quartz.
The melting of the pure quartz requires itself a crucible made from materials that resist to even higher temperatures, e.g. a crucible of molybdenum or even a crucible of iridium, for the lowest contamination with impurities.