"Nice to meet you. I am Minji."
Translation:처음 뵙겠습니다. 저는 민지입니다.
You’re right, that would be a literal translation. Nevertheless, I think the translation as “Nice to meet you” is fine based on how the phrase is used. When I think of 처음 뵙겠습니다, I think of a situation where I first address somebody of higher status for the very first time (maybe after a mutual acquaintance has introduced us). Then I would say: 처음 뵙겠습니다. 방아분이라고 합니다. Then maybe one more sentence to introduce myself, and then 만나서 반갑습니다 (or depending on the situation maybe 잘 부탁 드립니다 instead).
Unfortunately English doesn’t have a direct equivalent to this formula. You can say “nice to meet you” either before or after introducing yourself, and there isn’t really anything to take the place before if you put “nice to meet you” after (except a greeting maybe). You definitely wouldn’t say “I’m meeting you for the first time!” So I think a translation as “nice to meet you” is fine as the closest approximation in terms of conversation flow. But I do think there should be an explanation of the Korean pattern of introducing yourself in the tipps section.
As AbunPang mentioned you're technically correct but no one ever says "It's my first time to meet you." So the closest and most appropriate translation is "Nice to meet you." You can't translate language directly and it's a fallacy to interpret language in such a manner. Language should rather be localized to match the context.
처음(으로) - for the first time, 뵙다 - most formal version of 보다. However, 뵙다 in conjugation can only use 겠다 (and maybe something else, someone correct me if so). So the first sentence is saying "We're seeing each other for the first time." I've never heard someone say that before though. People usually say "반가워요" (I'm glad [to meet you]) or "만나서 반갑습니다" (Since we're meeting, I'm glad).
Do you mean something like 처음 뵙겠어? That doesn’t work because 뵙다 is already an honorific verb “to meet someone of high status”. So 처음 뵙겠습니다 is pretty much a fixed expression. If you want to use plain speech you have to switch idioms altogether. Something like 만나서 반가워. 난 민지야 should be accepted. Feel free to report it (using the flag button) if it’s not.