All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
We did not exactly understand what you meant by marrying off one's daughter before she gets the third menses. Perhaps what is meant is the third menses since she reaches puberty and first starts to menstruate. In any case, there is no evidence for this statement and it is not true.
However, a guardian should take the initiative to marry off the girl who is under his guardianship and the earlier the better as this protects her and keeps her chaste. For more benefit, please refer to Fataawa 116746 and 13907.
It should be noted that it is permissible for the guardian to offer his daughter in marriage to righteous men as ‘Umar ibn Al-Khattaab did regarding his daughter Hafsah .
Allaah Knows best.