According to rabbis Walter Jacob and Moshe Zemer (1932-211), engagement through sexual intercourse did not require witnesses, it was sufficient a declaration of the will to marry the woman:
"Marriage could and can still be effected through intercourse (biah) when preceded by a statement indicating the wish to take this woman as a wife or if two witnesses have seen the couple leaving for a private place. Marriage is assumed, as intercourse was taken for granted "(Marriage and Its Obstacles in Jewish Law: Essays and Responsa, Edited by Walter Jacob and Moshe Zemer, Berghahn Books, 1999 New York, p. 60).
Where does the rabbi get it from? So it was not necessary to have the presence of the two witnesses?
Maimonides (Sefer Nashim, Hilchot Ishut 3,15) further states that witnesses are not necessary if an agent is appointed (by the girl's father or by the spouse is meant?): "In all matters, a principal's agent is regarded as the principal himself, and there is no need to appoint witnesses "(Moses Maimonides, Mishneh Torah, A new translation with commentaries and notes, Vol. XVI, Hilchot Ishut, Translated by Rabbi Eliyahu Touger, Moznaim, New York 1994, p. 36).
Can you confirm that it is possible to have a betrothal without witnesses? I mean, does the law allow it?