The sentence "Yoroshiku onegai shimasu" (よろしく おねがい します) (宜しくお願いします) has other meanings besides "Nice to meet you." It can be translated very loosely as "I am looking forward to working together with you in happy cooperation." This is something we just don't say in English but it is quite often said in Japanese. Let's take a look at the following to see how よろしく おねがい します can be translated into English. Watch this video (mostly in Japanese only, with a little English here and there) as an English teacher is teaching English to Japanese speakers and see the many ways she translates よろしく おねがい します into English.
(Being the newest person to be hired at a place of employment or to join a group within the company)
I am looking forward to working with you.
I am looking forward to joining the company
I am looking forward to being part of the team.
We look forward to doing business with you.
(Greeting someone who has just arrived at a meeting at work)
Thank you very much for coming.
(The person who just arrived at the meeting)
Thank you for having me.
(Greeting the person who just arrived)
It's our pleasure.
I appreciate you coming.
I appreciate you taking the time to meet with us.
(Talking to a friend, or an employee of 'lesser rank' at work)
よろしく (only one word).
Thanks. (often paired with goodbye as in よろしく、バイバイ。)
(Asking a friend or an employee of 'lesser rank' to do something)
Thank you for doing this.
I'm counting on you.
I knew I could count on you.
(The lady actually has more phrases, some of which were left out here for brevity.)