Da'as as soul-illumination through avodah

בפסוק וידעו כי אני ה' כו' מא"מ לשכני בתוכם.

On the pasuk "And they shall know that I am Hashem etc." — they went out of Mitzrayim in order that I may dwell among them.

The whole purpose of yetzias Mitzrayim was so that Hashem's Shechinah should rest within Bnei Yisrael; the "knowing" of Hashem is itself the indwelling.

וכ"כ בתמיד במועדו כי הקרבת התמיד הי' כמו מועד.

And so it is written, "the tamid (daily korban) in its appointed time," for offering the tamid was like a mo'ed (a set time of meeting).

The daily korban created a fixed point of encounter with Hashem, just like a festival is a set time of closeness.

שהביא דעת בבנ"י.

For it instilled da'as (awareness of Hashem) in Bnei Yisrael.

The avodah of the korban drew an illumination of true knowledge of Hashem into the people.

ולזה נתקן תפלות במקום תמידין.

For this reason the tefillos were established in place of the daily korbanos.

Since the korban's function was to bring this awareness, tefillah now serves the same role of drawing da'as into us.

כמ"ש מחדש בטובו מעשה בראשית.

As we say, "He renews in His goodness, each day, the act of Creation."

The world is constantly being renewed by Hashem, and this renewal flows through a particular channel.

בטובו אלו ישראל.

"In His goodness" — these are Yisrael.

The Chazal read "His goodness" as a reference to Bnei Yisrael, who are the vessel for the renewal of Creation.

שהנשמה והפנימיות של מעשה בראשית הוא אצל בני ישראל.

For the neshamah and the penimiyus (inner essence) of the act of Creation rests with Bnei Yisrael.

The inner soul of the entire creation is found within Bnei Yisrael, who carry its hidden vitality.

ועל ידיהם התחדשות הבריאה.

And through them comes the renewal of Creation.

It is Bnei Yisrael, through their avodah, who awaken the daily renewing of the world.

וזה נעשה ע"י יציאת מצרים.

And this came about through yetzias Mitzrayim.

The Exodus is what empowered Bnei Yisrael to become this channel for renewing Creation.

לכן מזכירין יציאת מצרים קודם התפלה שבתפלה ממשיכין בנ"י הנשמה כמ"ש בזוה"ק ע"פ לא תאכלו על הדם.

Therefore we mention yetzias Mitzrayim before tefillah, for in tefillah Bnei Yisrael draw down the neshamah, as the Zohar HaKadosh explains on the pasuk "You shall not eat over the blood."

Recalling the Exodus before davening prepares us to draw the soul-illumination into ourselves through tefillah, just as the Zohar links the soul to that pasuk.

ובשבת קודש מוסף שיש בו נשמה יתירה וכן היא ג"כ זכר ליציאת.

And on Shabbos Kodesh there is Mussaf, which contains the neshamah yeseirah (the extra soul), and it too is a remembrance of the Exodus.

The added Shabbos tefillah corresponds to the extra soul of Shabbos, and like all our tefillos it recalls the redemption from Mitzrayim.

וכ' בשבת לדעת כי אני ה' מקדישכם.

And it is written regarding Shabbos, "to know that I am Hashem who sanctifies you."

Shabbos, too, is described in terms of "knowing" Hashem — the same theme of da'as.

הכלל בכל מקום שיש הארת נשמה נקרא דעת.

The principle is: wherever there is an illumination of the neshamah, it is called da'as.

Whenever a soul-light is revealed — in the korban, in tefillah, on Shabbos — the Torah calls that revelation "knowledge."

וזה המאמר נכתב בקיצור ממיעוט פנאי:

And this maamar was written briefly, due to lack of time.

The Sefas Emes notes that he recorded this thought in shortened form because he had little leisure to elaborate.

Summary: The purpose of yetzias Mitzrayim was for Hashem to dwell within Bnei Yisrael by instilling da'as — an inner soul-awareness. The tamid, tefillah, and Shabbos Mussaf all serve to draw this neshamah-illumination into us, since Bnei Yisrael carry the inner essence of Creation and renew it through their avodah.