three emunot

So, rav goldvicht this week brought a Maharal that talks about the three regalim as each epitomizing one of three foundational beliefs.
Pesach: belief in the existnce of God, or "ein od milevado."
Shavuot: belief in torah min hashamayim
Sukkot: belief in hashgachah peratit (or hashgochoh pratis).

Maharal ties these three beliefs to three times in the Torah where there is statement that all of benei yisrale (vs .specific individuals) belive s/t.
1- in egypt, the people believe (va-yeamen ha-am) that GOd has redeemed them (hashgachah peratit)
2- at yam suf, "va-ya'aminu baShem uvemosheh avdo (existence of God)
3- at har sinai, "ve-gam becha ya'aminu le-olam." (torah min hashamayim)
(citations may be coming when i have more time...)

ignoring for the moment some problems* with especially the third prooftext, i am wondering about the order:
the order of the regalim seems logical enough - belief in God as such, then belief in individual attention from said God, then belief that that attention has taken the form of, among other things, the Torah. but what about the order in history? how can b"Y believe in hashgachah before they believe in God as such?
There seems to be some statement here about the genesis of belief under suffering/extreme circumstances (egypt) as opposed to "ordinary" times. It makes some sense to say that one sees God in the details of redemption before one has the emotional (and physical) strength to see a "bigger picture," but I think there is probably more to say here. what does it mean to acquire, as a people, belief in hashgachah before basic emunah? Does that perhaps have something to do with the apparent ease w/ which b"y lose focus on God in teh desert and the necessity of frequent open miracles? Is our celebration of the chagim in their order some sort of an attempt to correct the original order?
Thoughts are welcome.

*eg, the statement is a promise that b"y will believe something., not a statement that they actually do.