Jisho

Try to think the other way around. The language was there first, and the characters are just used to write it down. So instead of saying that おお is used when reading 大きい, really 大 is used for writing おおきい.

So from this perspective, in Japanese you had the words たいした and おおきい and now you just need to come up with a way to write them. For both words, 大 was a fitting Chinese character. No matter the pronunciation of the words, because Chinese characters as you well know carry a certain meaning by themselves.

Think about what you would do if you needed to come up with a way to write English with Chinese characters. For example you might decide that the words big and large are now written as 大ig and 大ge. Makes sense, right? Sure, same character different pronunciation but every person that speaks English and knows the meaning of Chinese characters has a good chance of grasping what you’re going for.

(Disclaimer: actual history behind how Japanese writing system came into being is a lot more convoluted but the general gist is true. The spoken language preceded its written form. Always consider this, don’t forget it’s a language spoken by humans in everyday life, it’s gonna be as chaotic as every other human language. Also if you’re interested I would recommend learning more about the details of how Japanese writing evolved historically, knowledge about that can be a help with understanding the modern writing.)

凄い話したよ。分かりやすくになりました：）