Комментарий к Шмот 19:17

לקראת האלהים [AND MOSES BROUGHT FORTH THE PEOPLE …] TO MEET GOD — This (the word לקראת, “to meet”, which is used when two persons are approaching one another) tells us that the Shechina was going forth to meet them, as a bridegroom who goes forth to meet his bride. This is what Scripture means when it says, (Deuteronomy 33:2) “The Lord came from Sinai”, and it is not said, “[The Lord came to Sinai” (Mekhilta d'Rabbi Yishmael 19:17:1).

לקראת האלוקים, toward the army of angels forming the entourage of the Divine presence, in anticipation of the descent of the Shechinah on the mountain in verse 20.

ויוצא משה את העם, Moses lead out the people, etc. Perhaps this was necessary because the people had become afraid of the Mountain by now. Moses took them to the edge of the Mountain so that they would accept the Torah while standing there.