The first 20 verses of the 12th chapter of Sh'mot is Hashem's speech to Moshe and Aharon concerning the mitzvot that prepare B'nei Yisrael for Makkat B'chorot. In verse 11 it is written:
יא וְכָכָה֮ תֹּֽאכְל֣וּ אֹתוֹ֒ מָתְנֵיכֶ֣ם חֲגֻרִ֔ים נַֽעֲלֵיכֶם֙ בְּרַגְלֵיכֶ֔ם וּמַקֶּלְכֶ֖ם בְּיֶדְכֶ֑ם וַֽאֲכַלְתֶּ֤ם אֹתוֹ֙ בְּחִפָּז֔וֹן פֶּ֥סַח ה֖וּא לַֽיהוָֽה׃
It seems that the entire procedure of the korban pesach in Mitzrayim, culminating with its consumption, was to demonstrate B'nei Yisrael's rejection of Mitzri idolatry. Why was it necessary for them to eat the korban pesach fully dressed for their journey and with, חִפָּזוֹן, great speed?
I believe the simple explanation is that it was in order to demonstrate their absolute conviction that Hashem would immediately redeem them (see Seforno). However, there does seem to be another lesson: to further demonstrate Pharaoh and Mitzrayim's lack of power before Hashem.
Let us consider the following scenario: Pharaoh is defeated. What would we expect to happen next? Most likely many months of talks and negotiations hammering out the precise terms of the defeat, how the slaves will be released, what reparations B'nei Yisrael will receive, prosecution of those who committed crimes against humanity, etc. Even more time would be spent planning out the best way for B'nei Yisrael to leave Mitzrayim and make the long journey to Eretz Yisrael. In other words, one would think that even if Pharaoh were defeated it would still be necessary to go through a slow diplomatic process - nothing can happen overnight in politics.
The geula from Mitzrayim was different - it did not occur through any know causal structure - it did not occur by playing to a pompous bureaucracy. Perhaps this is one of the meanings of "lo al y'dei malach" - not through any know causal system - it was HaKadosh Baruch Hu:
וַיּוֹצִיאֵנוּ ה מִמִּצְרַיִם--לֹא עַל יְדֵי מַלְאָךְ, לֹא עַל יְדֵי שָׂרָף, לֹא עַל יְדֵי שָׁלִיחַ, אֵלָא הַקָּדוֹשׁ בָּרוּךְ הוּא בִּכְבוֹדוֹ: כְּמוֹ שֶׁנֶּאֱמָר "וְעָבַרְתִּי בְאֶרֶץ מִצְרַיִם, בַּלַּיְלָה הַזֶּה, וְהִכֵּיתִי כָל בְּכוֹר בְּאֶרֶץ מִצְרַיִם, מֵאָדָם וְעַד בְּהֵמָה; וּבְכָל אֱלֹהֵי מִצְרַיִם אֶעֱשֶׂה שְׁפָטִים, אֲנִי ה" שמות יב,יב
The entire power structure of Mitzrayim was reduced to rubble. The immediacy of their exodus further demonstrated this breakdown. B'nei Yisrael demonstrated their absolute trust that Hashem would take them out of Mitzrayim immediately as a direct result of eating the korban pesach.