As a Chinese native speaker who knows a little bit about Japanese, I would like to talk about this character on a Chinese perspective. I believe the origin of your question can be traced to the Chinese origin.
Picture source: http://www.fantizi5.com/ziyuan/ and then search "前".
Translation: Original character: (止 over 舟). This character is from 舟 and 止, where 舟 is a boat, and 止 is a foot, indicating the boat is going forward.........
Consider duck, which is an animal that uses its feet to pedal, 舟 with 止 should be considered as a person using his/her feet to pedal the boat to go forward.
In Chinese, 前 has almost the exactly same meaning as in Japanese - the first is something in front of something. E.g.: 面前, which literally means "in front of the face", or just "in front of (a person)"; 站前, which is used by many cities as "the area in front of the (main) train station". This can be considered as a priority queue (sorry, but I'm a computer scientist, and this is a computer science term, but I do think it is not hard to understand), 前 means A has a higher priority than B.
The second meaning is about time - which means "before". However, in Chinese, 前日 means "the day before something happens" (e.g.:结婚前日, "the day before wedding"). Interestingly, 前天 means "the day before yesterday", though people usually treat 日 and 天 as two characters with the same meaning. More interestingly, "先前几天/先前几日" in Chinese both have the same meaning: "preceded days before today (or someday)", "昨天/昨日" both mean "yesterday". Nevertheless, 前 means "preceding time". Time can also be considered as a queue - the preceded time can be considered as having a higher priority. Or front another perspective, the preceded time is "in front of" the following time.
Another meaning is "proceed". For example: "前进" literally means "proceed forward", which means "proceed". When proceeding, it means to get higher priority.
All in all, 前 means "a higher priority" as a state/time/etc, or "to get a higher priority". Therefore, it means going forward.
I saw someone said that he/she is "always confusing the meanings of 先日 and 前日" in Japanese - it's normal, as you can see from above, they are complicated from the root (which is Chinese itself) of this question.
P.S., for Chinese, the words with "天" that can be changed to "日" without changing the meaning (e.g. "昨天/昨日", "先前几天/先前几日", "三天/三日 (three days)", "星期天/星期日 or 周天/周日(Sunday, 周天 is rare, 星期天 and 周日 are most used, 星期日 is a little bit formal)", "工作天/工作日(Weekdays, though the first one is rare)"), the one with "天" is more informal, and the one with "日" is more formal. Even for most words with "日" that is not interpreted as "day" (e.g.: "日" itself can either mean "sun" or "day" (and sometimes can be used as f-word in Chinese), but "天" only means "day"), it's more formal than its synonyms (e.g.: 日 vs 太阳, both mean "the Sun", and the first one is more formal; same when interpreting "日" as a swear word, it is more formal than its synonyms).
It's hard to feel the inner meaning of a word when learning another language. I personally learn English (since 2001-2002, when I was 4-5) and German (since 2014), and I do speak better English than most of my Chinese friends - but still worse than real native speakers...... It is necessary to be soaked in that environment in order to be a better user of one language.