How long will it take for China to take control of the Taiwanese territory if war breaks out?

Anywhere from a couple of days to never.
The key to how things go are going to be logistics, logistics, logistics.
Taiwan is an island in an ocean. meaning whoever controls the ocean around Taiwan, will control Taiwan.
Now remember an area called Guadalcanal? it had been an island where the waters around became the key to the island.
This is Iron Bottom Sound. each side lost 24 major warships fighting for control of the ocean round the island.
By User:W.wolny, Upload from German wikipedia by user:Vvulto - Own work, CC BY-SA 3.0, File:Wrecks within the Ironbottom Sound.jpg - Wikimedia Commons
That was an island within the Pacific too. The fight for the island was decided by who could supply their army the simplest . for each Marine that died fighting on the island 3 USN sailors died off shore.
The US won because with Henderson Field the Imperial Navy couldn't stay in these critically important waters after the sun came up. in order that they spent the “Slot” a passage between two groups of islands, and delivered supplies in oil drums crammed with food, and bullets, dropped over the side and fished out by swimmers.
It is little wonder that the japanese soldiers called it Starvation Island.
This time China has Henderson Field. it's going to be far too politically dangerous for US assets to attack China .
We would , after all, be committing a blatant act of war if we attacked Chinese facilities on the Mainland.
But the PLAN and PLAAF will still need to run ships into the island and deliver replacements, and supplies. YES they will fly during a lot. Its just the large heavy things, the massive bulky items, will still got to be delivered by ship.
Look for many ship to ship action during this conflict. Again a bit like Guadalcanal.
China will need to await the Winter Olympic Games to finish . to attenuate disruption from a USN blockade of her ports she is going to got to complete an pipeline from Iran to China, via Russia.
At that time i think all bets are off.