There is Pinyin, the official romanisation of Mandarin Chinese, in which for example "汉语拼音" becomes "hànyǔ pīnyīn". So, one could write using that. The argument typically is that Chinese has too many homonyms to make that practicable. I'm not sure I buy that, as spoken Mandarin is presumably intellegible, despite those homonyms.
There's a lot of info in the informative book The Chinese Language: Fact and Fantasy by John DeFrancis, and on this website: http://www.pinyin.info
> But surely writing speed must be slower.
I've found that that is not the case. While a typical character is more complex than a typical letter, you need fewer of them. At uni, I tested that with a native Chinese speaker and a native German speaker. We chose several random English sentences, they translated them into their respective language, and then we timed how long they took to write them down (by hand, in Chinese, German, English). It was basically the same, no systematic difference.
> How do chinese people even type?
There are several input systems, some based on pronunciation, some based on the shape or strokes.
See https://en.wikipedia.org/wiki/Chinese_input_methods_for_comp...
or https://www.hackingchinese.com/chinese-input-methods-a-guide...
Emacs has 25 kinds of Chinese input methods.
A speaker at Stanford on the topic of early keyboards used for Chinese noted graph structure such as the one you find in Canjie input method was what they used before soundspelling. Today, hypergraphtext autocompletion influences message contruction on flatscreen devices in a kind of mind-machine blend mode on a massive scale.