A lot of the hand wringing about "muh amphib operations difficult. China will never succeed" is fair if you look at warfare from WW2- Desert storm. However times have changed. To explain this further we need to understand how war was fought for most of the 20th century and how that is rapidly changing in the 21st century.
For land warfare in the 20th century there were 3 combat arms in the ground force which are : infantry, tanks/armour and artillery. This then makes 2 broad parts of land warfare that are interconnected which is : firepower and manuvere. Firepower is almost entirely done with artillery and manuvere is done with infantry and armour in conjunction.
Arty and firepower is easy to understand. Just shoot more shells more accurately then OPFOR and you can create greater effects. The initial role of arty should be to do counter battery to prevent enemy firepower (their artillery) from destroying your maneuverer elements (your tanks and infantry). If you have spare firepower left over you should use it on OPFOR manuvere elements (their armour/infantry) and attriting/fixing them - which is why for offensive pushes you should have much more arty than OPFOR as you need to not only to defang enemy arty but also make life hell for their armour and infantry. Firepower is at the rear whilst manuvere elements take a frontal role .
With regards to Manuvere elements which are armour and infantry this is where a lot of hand wringing about flexible "mission command" and whatnot comes from. You want these elements to be able to make offensive decisions on the fly whilst also being well trained in actual usage of their weapons. There are 3 steps for your manuvere elements to employ :
(1) Choose one of the 7 maneuverer unit formations :
1) Column. 2) Line. 3) wedge . 4) Echelon(left or right). 5) Vee. 6) Diamond. 7) Box.
(2) Choose a Movement Technique:
1) Traveling 2) Traveling overwatch 3) Bounding overwatch.
(3) Choose one of the 5 forms of maneuverer : 1) Frontal attack. 2) Penetration. 3) Envelopment 4) Turning movement. 5) Infiltration.
Whosever armour and infantry can cycle these 3 elements quicker and better than OPFOR will win the manuvere element.
However modern warfare is changing rapidly. Modern land warfare is effectively becoming very similar to air and naval warfare in that its becoming about a sensor-shooter complex.
The proliferation of modern sensors (drones) and prompt cheap precision fires (cheap pgms, suicide drones, HIMAR GMLRS/Excalibir) is changing modern warfare. Instead of having to wait for hundreds of thousands of shells to create effects on OPFOR and fixing them then neutralising them with manuvere the better army will be able to deploy numerous UAS's to find OPFOR and then immediately cue/direct a PGM. This should be able to be done quicker and cheaper than a logistically burdensome artillery supply chain and an expensive training regimen.
In terms of people screeching that "REEE AMPHIB OPERATIONS IMPOSSIBLE. TAIWAN NUMBA 1" they are looking at warfare through a 20th century lens. In the 20th century where the PLA wouldn't have access to very powerful sensors that can direct very cheap pgms to destroy the ROCs tank artillery etc then sure trying to land millions of shells across a hundred mile strait would be pretty difficult but the thing is China with their gargantuan ISR complex over Taiwan providing 24/7 coverage can simply cue thousands of piston based suicide drones, PHL 16 guided 370mm and the KD series pgm. They can do all of this from the comfort of the mainland without having to land a single troop in Taiwan and destroy the majority of the ROCs tanks, artillery and forts for the infantry for the ROC. In short weapons have gotten a lot more technologically advanced over the past few years due to rapidly advancing sensors and more accurate fires being available. There is nothing stopping the PLA in the first few weeks to destroy as much of Taiwan's force as possible such that they would be entirely reliant on infantry which can be cleaned up as soon the PLA lands as infantry without supporting arms are sitting ducks.
Technology has indeed changed, and it is not POSSIBLE for PLA to win in a Taiwan contingency, but I think it is a matter timing, overwhelming firepower within an extremely short span of time (hours, not even days), COMPLETE incapacitation of blue forces (especially air defences) within hours before reinforcements (from US and Japan) could mobilize, and capture of key landing spots (especially ports for unloading armour) BEFORE the arrival of reinforcements. If the PLA cannot achieve all of these objectives within hours after the first barrage, China could risk losing the war before it even starts. In other words, the PLA would need to completely establish new status quos in Taiwan within a few hours completely to its favour. Or the situation would just turn into a war of attrition (with full US, Australian, Japanese, and Indian involvement, so two front war for China) lasting months before returning to status quo ante bellum. The current ROCA strategy is for Taiwan to last for at least a week, and the PLA's job is to stop that within a matter of hours. Otherwise as soon as the QUAD gets its forces in order and start flying to toward Taiwan (in Jai Hind's case, open up a new front in the Himalayas), it would be game over. . Thus, I believe it is possible to win, but the first wave of attack better punch above its weight, or else...
As with amphibious landings, the PLARF and the PLAGF's PCL-161 units (and PLAAF units as well) would need to closely coordinate with the landing force to "clean" the proximities of each landing sites and ports with cluster and thermobaric munitions. The amount of joint force collaboration and firepower needed in this scenario would be unprecedented even for the US military.
Honestly, the speed, firepower, and joint-force collaboration needed in this scenario would be unprecedented in human history. Definitely extremely challenging for the PLA, but it is not impossible.