The rush is to try to take the island before any outside force can intervene.They are not going to use many ballistic/cruise missiles on Taiwan. They have PCL191, PGMs and stand off missiles that can do plenty of damage. There are several hundred targets in Taiwan that they will need to hit and that doesn't even include all the gas stations. That will require a couple of thousand rockets, guided missiles and ground attack missiles to degrade. Not something you can do in a couple of days. Taiwanese artilleries will be waiting for PLA the moment they try to land. I'm not really sure the rush to do this? China's great advantage right now is in its EW capabilities and its drones. Militarized drones can do a lot of damage over Taiwan once they establish complete air dominance. I'm not sure why you are so eager to land when defending force has high morale and committed to fighting vs when they are exhausted and deflated.
Anyhow, another post from Lyle Goldstein
China understands the need to attack/disable command centers, reconnaissance and early warning system. Expect them to have enough missiles to take all of this out. Russia has been fight at a disadvantage because it hasn't destroyed enough Ukrainian command centers and also unwilling to attack American ISR targets that are giving precious intel to Ukraine. China will go after these assets very early on.
Do we have any information on how many rockets, missiles, suicide drones etc China can launch in a single day? Because if it's possible to kill all fixed targets in a single day, that's what I would do. If the entire defence infrastructure on the island goes up in smoke in a single day and the PLA has already landed on the beaches, the defending force won't have very high morale. That's the principle of shock and awe. But maybe my assumption that China has many hundreds of missile launchers is wrong. If you add up PCL191 launchers, DF15 ballistic missiles and all the missiles on the PLAN ships close enough to Taiwan, shouldn't it be possible to launch 1000 or more on the first day? On top of that you'll have PGMs from the air force. Only 10 Type 052D destroyers by themselves should have a theoretical maximum capacity of 640 missiles if they only stored land attack missiles. So I don't understand why you'd need two months.