Reawakening Har Sinai
בפסוק עולת תמיד העשוי' בהר סיני
Regarding the pasuk, "a continual olah-offering that was made at Har Sinai" (Bamidbar 28:6).
The Sfas Emes opens with the verse that describes the daily korban tamid as something that was "made at Har Sinai," hinting that the offering is rooted in the events of Matan Torah.
פי' שבעת עמידת הר סיני נתקרבו בני ישראל להשי"ת לדורות עולם כמ"ש רז"ל כל מה שנביאים התנבאו קבלו מהר סיני וכן כל ת"ח שבכל דור ודור ע"ש
The explanation is that at the standing of Bnei Yisrael at Har Sinai, they were drawn close to Hashem Yisbarach for all generations of the world, as Chazal said: everything that the prophets prophesied, they received from Har Sinai, and likewise every talmid chacham in each and every generation — see there.
He explains that the great closeness to Hashem achieved when Bnei Yisrael stood at Har Sinai was not a one-time event but a wellspring fixed for all generations, which is why both the prophecy of the nevi'im and the Torah of every talmid chacham in every generation flow from that moment.
ולכן כל העשיות שבנ"י עושין תמיד הכל רק לעורר הכח של מעמד הר סיני:
Therefore, all the actions that Bnei Yisrael perform continually are entirely only meant to awaken the power of the standing at Har Sinai.
Consequently, every deed that Bnei Yisrael do throughout their lives — like the continual korban tamid — is essentially meant to reawaken and draw down the power and kedushah of that standing at Har Sinai.
Summary: The Sfas Emes takes the phrase describing the korban tamid as "made at Har Sinai" and reads it as a teaching about the enduring nature of Matan Torah. When Bnei Yisrael stood at Har Sinai, they were bound to Hashem Yisbarach for all generations, so that every later prophecy of the nevi'im and the Torah of every talmid chacham in each generation is drawn from that very standing. Because that closeness remains the source of all kedushah, every continual action of Bnei Yisrael is in truth meant only to reawaken the power of Har Sinai. The daily tamid thus becomes a model for all of avodah: a constant renewal of the bond first forged at Sinai.