Subsequent dan grades in judo are named numerically nidan (二段), sandan (三段) etc, but the first grade is called shodan (初段) "beginning grade". Is there a particular reason for this as opposed to the expected ichidan (一段) "first grade"?
初 can also be pronounced "hatsu", which is used interchangeably to mean "start", "beginning" or "first". For example, hatsutanjō is a baby's "first birthday" and hatsuyuki is the winter's first snow.
Technically speaking, "sho" is the kan-on reading of the Chinese character 初, while "hatsu" is the kun-yomi reading of the same kanji. The kan-on reading is generally a Japanese approximation of how the Chinese would pronounce the character (in this case, "chu"), while the kun-yomi reading is how Japanese speakers would natively pronounce the same kanji. Even in Chinese, however, one of 初's main definitions is "first".
It is also good to note that "ichidan" does not mean "first dan", but rather "one dan", just like "nidan" means "two dan" and so on. This is because the Japanese numbers used in this context are numerals, and not ordinal numbers. Ordinal numbers in Japanese use the traditional Japanese numbers (hitotsu, futatsu, mittsu, etc.) as a base, to which the suffix "-me" is added. In Japanese, thus, you are not a first/second/third/etc. degree black belt, but rather a black belt that has 1/2/3/etc. degrees.
Why is "ichidan" not used for the first degree? I'm afraid I have no other answer than what my former karate sensei told me. According to him, you don't actually need to count the degrees if you only have one, and insisting on counting your single degree could be interpreted as bragging. In this context, "shodan" conveys more meaning, as it can both mean "first degree" and "beginning degree". Thus, it marks the start of a journey towards mastery rather than mechanically counting the single degree you hold.
Now as to why "shodan" instead of "hatsudan" (hatsu being more frequently used in compound words meaning "first something" than sho) or even "hitotsume dan", I have no idea.
I have no explicit evidence to back this up, but I suspect this was to avoid ambiguity with the homonymous superlative adverb 一段 (いちだん), which might lead people to assume 1st dan is the highest dan grade (cf. 1st kyu), as opposed to the starting one.
Note that the use of shodan predates judo and is terminology inherited from Go.1 2
1. Das "go" - spiel (1880)
2. An unabridged Japanese-English dictionary, with copious illustrations (Dan; Shodan) (1896)