I would like to propose a wonderful explanation based on a fundamental idea that is repeated over and over in the teachings of Chazal. At Matan Torah, HKB”H designated Yisrael as his bride. As we have learned in the Mishnah (Ta’anis 26b), they expounded on the passuk (Shir HaShirim 3, 11):
"צאינה וראינה בנות ציון במלך שלמה בעטרה שעטרה לו אמו ביום חתונתו וביום שמחת לבו, ביום חתונתו זה מתן תורה, וביום שמחת לבו זה בנין בית המקדש שיבנה במהרה בימינו".
“Go out and gaze, O daughters of Tziyon, upon King Shlomo adorned with the crown his mother made him on the day of his wedding and on the day of his heart’s joy.” “On the day of his wedding” refers to Matan Torah; “and on the day of his heart’s joy” refers to the building of the Beis HaMikdash—may it be built speedily in our days.
We find a similar elucidation in the Midrash (D.R. 3, 12) concerning what HKB”H instructed Moshe when preparing Yisrael for Matan Torah (Shemos 19, 10): "לך אל העם וקדשתם"—go to the people and prepare them. With the term "וקדשתם", HKB”H was appointing Moshe Rabeinu to be his agent to wed Yisrael with the giving of the Torah. This is corroborated by the following passuk (ibid. 17): "ויוצא משה את העם לקראת האלקים מן המחנה"—Moshe took the people out of the camp toward G-d, and they stood beneath the mountain. Commenting on this passuk in the name of the Mechilta, Rashi says that the Torah is telling us that the Shechinah went out to greet them like a bridegroom going out to greet his bride.
It is fitting to introduce what we have learned in the Mishnah (Kiddushin 2a): "האשה נקנית בשלש דרכים... בכסף בשטר ובביאה"-- a woman is acquired in three ways . . . she is acquired with money, with a document, and with intimate relations. In his commentary on the passuk (ibid. 19, 4), the Ba’al HaTurim interprets HKB”H’s statement to Yisrael: "ואביא אתכם אלי"—and I brought you to Me—to mean that HKB”H wed Yisrael with all three. The spoils of Mitzrayim were the money; the Torah was the contractual document; “I spread My wings over you . . . and I entered into a covenant with you,” was the spousal relations. Therefore, the prophet Hoshea (Hoshea 2, 21-22) employs the term ״וארשתיך לי״ –“I will betroth you”—three times.
Now, when the Ba’al HaTurim writes that HKB”H consummated His marriage to Yisrael with spousal relations (cohabitation), he is clearly referring to the Mishkan; there HKB”H met with Yisrael in intimate, close quarters. As the passuk states (Shemos 25, 8): "ועשו לי מקדש ושכנתי בתוכם"—they shall make Me a sanctuary, so that I may dwell among them.
This is further evident from the passuk (ibid. 18): ועשית שנים כרובים זהב מקשה תעשה אותם משני קצות הכפורת—you shall make two “keruvim” (cherubim) of gold—beaten shall you make them—from both ends of the “Kapores” (lid). Rabeinu Bachayei comments that simply understood, the two “keruvim” were a male and a female. He substantiates this assertion by referring to the Gemara (Yoma 54a): "אמר רב קטינא, בשעה שהיו ישראל עולין לרגל מגללין להם את הפרוכת ומראין להם את הכרובים שהיו מעורים זה בזה, ואומרים להם ראו חיבתכם לפני המקום כחיבת זכר ונקבה". Rav Katina said: When the people of Yisrael would ascend on the festival, the kohanim would roll up the “parochet” for them and show them the “keruvim” which were joined together in an embrace. They would say to them, “Behold your affection before the Omnipresent, like the affection of a male and a female.”
