Yes, but not immediately - it could be in a few years. You would use this expression when estimating their age, rather than when predicting their birthday.

I don't know what smb is, but we would say anything from 57 is pushing 60. Think of it like when you round numbers although with less accuracy. If someone/something is nearer 60 than 55, they are pushing 60. It's an estimate. It is also used in speed, that car has got to be pushing 60 (mph)! So again, getting close, if not there. Think of it as 'approaching' 60.