'Context' includes things like: Why does this friend want this translated? Is he/she translating a manga? Is he/she planning on texting someone with this? Unless you know the purpose it's kind of meaningless asking 'how to translate this phrase'.
Personally, I would say something like 我等他给我发短信。要不我主动一点，从我这边先给他发。Probably not terribly idiomatic, and in fact, 主动 is quite different in its connotations from 'mature'. It means 'be aggressive' rather than sitting around waiting for the other person to take the first step. 'Be mature' sounds like a young person admitting that they shouldn't be so sulky or resentful (setting emotional traps) and making a move from their own end. Quite a difference. But I really don't know what the Chinese equivalent for 'being mature' in a situation like this is.