Firstly, the question is extremely unrealistic. 10-12 hours, specially when the two are considered major forces in the world. Even US took more time to completely control Iraqi Air Force, and here we are talking about India. All the hate aside, Indian Air Froce is a formidable force and should not be underestimated.
In my opinion, there were three main objectives Chinese had in mind when they initiated small incursions in various territories they think belong to them:
1 - Pressuring India to not take sides between West Vs Chinese alliance;
2 - Telling India and the UN, that unilateral action in Ladakh, Jammu and Kashmir is not acceptable, and Chinese are ready to move in and take what's rightfully theirs; and
3 - Helping Pakistan in securing CPEC by forcing India to spread its forces across north-eastern border.
Neither India, nor China wanted to convert the issue into a larger conflict although India had the reason and motivation to push China little bit. The reason was that China effectively denied India access to some pieces of land that earlier Indians had access to, and motivation was from the anti Chinese western alliance that had two of their own objectives in mind, (1) support their respective economies through Indian purchases in case of war, and (2) weakening China after pushing her to an unwanted war. Unfortunately, India didn't play according to their game plan and accepted a new status quo in the area on Chinese terms.
As much as Pakistanis wanted this war to happen (because we had our own objective of entering into IOJK and take whatever we could in the process), we should appreciate that Indians didn't take the bait for a small barren piece of land, and also managed the perception very well internally that they have come out as victors after the conflict.
In the last couple of decades, what I have personally realized that India is not in favor of (or lack the courage to enter into) all out wars with any country in the region. India had the best chance against Pakistan in 1999, when China was not technologically that strong, and the possibility of Chinese support was minimal. India didn't convert the localized Kargil skirmish to a full fledged war. Subsequent events also proved that India lacks the will of attacking Pakistan. In 2002, then in 2008, and then in 2016, and after that 2019, India avoided a full scale war against a much smaller enemy. India also didn't give any reason to Pakistan to expand the conflict. For example, in 2016, Pakistan was shocked at the drama of fake surgical strikes that was aimed at calming down the masses in India rather than irking Pakistan. In 2019 too, India didn't miss the target because of error, it was a deliberate calculated miss not to avoid giving any reason to Pakistan to respond heavily and forcing India to retaliate at a full scale. Here, I am not saying that India was not in a position to retaliate, but it lacked the will to enter into a full scale war against any country. Some say that India changed its priorities and wanted to follow Chinese rise and that is the main reason for avoiding a larger conflict with Pakistan.
Now, if India wants to avoid a full scale war against Pakistan, we shouldn't be expecting her to behave differently against a much larger enemy.
Now that we have discussed the possibility of war between China and India, lets discuss what if a war really breaks out between the two countries. So in case of a war, India (or even China) will never put all their forces against each other. Also, there will be a very very limited role of air forces in such a terrain characterizd by high mountains. In such a region, it takes a heavy toll on ground forces too and the chances of making changes in the border remain quite thin.
Now there are three other factors that may play a role in the conflict (not necessarily a war in the strict sense):
1 - Naval forces and their distribution across Indian ocean and SCS
2 - Electronic warfare
3 - Proxy war
We know that China has effectively achieved a couple of her objectives that I have listed above. I am not sure about Indian decision on anti Chinese alliance. In my opinion, India will show her teeth but will never become a proxy of western alliance against China. Indian decision makers are not naive to take sides in the conflict. They didn't even put their soldiers in Afghanistan where they had absolute confidence of a western walk over all the way. Against China, there is more a possibility that India is isolated by the regional countries, including Russia and those with shared borders. Isolation in the region is more disadvantagous than global one, because you can't just pick your land and put it somewhere else to avoid humiliation. India is anxiously looking towards leaving western forces from Afghanistan, and growing influence of China in her neighbors. In this scenario, it will be an extremely foolish mistake of taking side between west and China. So naval forces placement against China is out of question for now.
Electronic warfare, yes it might play a role like it did on 27th Feb, however, since the arial combat is almost out of question, that will not come into play. In case of an unlikely war, the west will support India in whatever way possible and that will be detrimental to Chinese interests too.
The third one is proxy war in which India has achieved some form of expertise. India will try to help west by motivating forces in Tibet against China and will try to bleed her through small cuts.
Therefore, in my opinion, we should wait for India to start a proxy war with western media on her side against China like how they have been doing in Pakistan for decades.
