Radicals like index/directory, but not first letter (in most cases).
I suggest you go to a library or book shop to borrow / buy a Chinese dictionary (paper format). Or, visit here to experience the online dictionary. The experience will be more direct than the text explanation.
In the other answer, I mentioned that the dictionaries in China are arranged by Pinyin.
A a 阿 an 安 ang 昂 ao 奥 …
B ba 八 爸 bi …
…
Z za 匝 …
So if you know the pinyin of 你 is nǐ, you can directly turn to N, just like what you do in English dictionaries. So the “first letter” of 你 is N (“你”字的音序是 N). Sometimes, if you need to arrange list of people's names, arranging in Pinyin of surname (以姓氏音序排序) is common. B 白冰; C 陈丽华; L 李琦; O 欧阳爽; W 王勇; Z 张志远. (The other common methods is arranging in the stroke number of surname 以姓氏笔画数排序: 2 丁利; 4 王勇; 5 白冰; 7 陈丽华)
If you don't know the pinyin of the characters, you then have to guess the radical, just like you need to guess the quotient of 52 ÷ 7; maybe it is 8, 8 × 7 = 56, it is larger than 52; let's try 7, 7 × 7 = 49, 52 - 49 = 3; therefore 52 ÷ 7 = 7 R 3.
Native speakers know some commonly used radicals in elementary school. For character 你, native speakers apparently knew that 亻 is a radical, but 尔 is not a radical. How do they learn to guess radicals faster? Their elementary school teacher will give them some skills / tips. But, if there are two radicals, the dictionary is usually included at the same time, but the one that is not recommended is marked with ° sign (even some dictionaries do not mark it).
Traditional Chinese dictionaries in Taiwan usually arrange the characters by Bopomofo (注音|zhùyīn) such as ㄅ (b in Pinyin), ㄆ (p in Pinyin), ㄇ (m in Pinyin), ㄈ (f in Pinyin). Cantonese dictionaries usually arrange the characters by Jyutping (粵拼|yuèpīn), which is a phonetic alphabet in Latin script (A-Z) designed for Cantonese. But all these dictionary offer radicals index/directory.
Note: I cannot guarantee that there is no dictionary arranged pages by radicals. But Pinyin, Bopomofo and Jyutping are common.