Immediately prior to Hashem's acceptance of Moshe's plea for total forgiveness and His continued presence among Bnei Yisroel, Moshe supplicates, "Please show me Your ways, and I will thereby know that I have found favor in Your eyes.." (Shmos 33:13) Targum Yonasan ben Uziel explains that Moshe asked God to reveal why the righteous suffer and the wicked prosper (from Peirush Yonasan, ref. Berachos 7a). The Sforno interprets that Moshe requested of Hashem to disclose other secrets of His mastery of the universe: how Hashem creates physical beings from naught and how Hashem enables beings to have free will despite His omniscience.
Why were these theological questions part of Moshe Rabbeinu's attempt to obtain God's favor? Similarly, why did Moshe ask Hashem a few pesukim later, "Please show me Your glory" (ibid. v. 18), whereupon Hashem hid Moshe in a cleft while Hashem enabled Moshe to intimately encounter His Presence. What do Moshe's probing theological questions and his special Divine encounter have to do with teshuva for the Chet Ha-Egel and the plea for God to continue to accompany Bnei Yisroel? Would more elaborate tefillos for forgiveness not have been more appropriate?
As was explained in an earlier dvar Torah in this series, the Jewish People had taken Hashem's Presence for granted; this is what led to the Chet Ha-Egel. Hashem bestowed upon the Jews objective manifestations of kedusha at Har Sinai and via the Mishkan, and the people - who had never truly sought nor longed for Hashem - failed to appreciate the gift of His Presence. The rectification of the Chet and the attitude which precipitated it was for Bnei Yisroel to seek and pine for Hashem's Presence. The relationship with God had to be bi-directional; the people now needed to approach and draw near to Him in order to merit the dwelling of His Shechinah in their midst.
But how does one do this? How does a person draw near to and pursue God? One cannot experience God with his senses, and God has no geographic location where one can go and seek Him. What is the method of drawing close to Hashem, and how were Bnei Yisroel expected to employ it?
Since Hashem lacks any physicality and cannot be perceived with human tangible senses, one must approach and encounter His Presence with the non-tangible aspects of the human experience - the intellect and the soul - and this is precisely what Moshe Rabbeinu, as the emissary of Klal Yisroel, did in his dialogue with the Divine.
Moshe sought for God to reveal the secrets of His mastery of the universe: how people are rewarded or punished, although from a limited, human perspective it cannot be fathomed, or for the mysteries of Creation and God's Omniscience to be disclosed. By posing these questions, Moshe drew near to Hashem via the intellect, seeking to be close to Hashem through Divine, inscrutable wisdom. Moshe also requested that God enable him to experience His glory. This represents the second method of approaching Hashem, through the soul. Moshe asked that he be in God's proximity in a spiritual sense, such that his neshama encounter Hashem's Presence with a proximity never before possible for a human being.
God responded totally favorably to Moshe's request for forgiveness and the manifestation of His Shechinah by approaching Him through the intellect and spirit. Bnei Yisroel, through the agency of Moshe Rabbeinu, had come full circle and demonstrated their love and attachment to God, Whose Presence they longed and pined for, thereby rectifying the Chet Ha-Egel and enabling Hashem to forge a new covenant that would last forever.