Does masturbating speed up/start puberty in young girls?

Neither....masturbation is normal for people at many ages and has nothing to do with bringing on or speeding up puberty. It's quite common during the pubertal years, but children often masturbate prior to that, as do adults.

No. Masturbation is similar to typical sexual activities with other people, but during masturbation other people are generally absent. A girl's pubertal process is a hormonal balance that changes over time, and is not aware of the presence or absence of other people. Masturbation is safer than typical sex (less psychological stress, no legal/moral/ethical issues, because other people are absent).