Can a Man See God?

El sueño de Jacob by José de Ribera (1638). Genesis 28 narrates Jacob’s dream at Bethel, wherein he saw Yahweh standing at the top of a stairway leading into heaven.

The answer, according to the Hebrew Bible, is pretty clear.

(All translations from the Hebrew are my own.)

וַֽיִּשְׁמְע֞וּ אֶת־קֹ֨ול יְהוָ֧ה אֱלֹהִ֛ים מִתְהַלֵּ֥ךְ בַּגָּ֖ן לְר֣וּחַ הַיֹּ֑ום וַיִּתְחַבֵּ֨א הָֽאָדָ֜ם וְאִשְׁתֹּ֗ו מִפְּנֵי֙ יְהוָ֣האֱלֹהִ֔ים בְּתֹ֖וךְ עֵ֥ץ הַגָּֽן׃
And they heard the voice of Yahweh God as he was walking in the garden in the breeze of the day. So the man and his wife hid themselves from the face of Yahweh God in the middle of the trees of the garden. (Gen. 3:8)
וַיֵּרָ֤א יְהוָה֙ אֶל־אַבְרָ֔ם
Then Yahweh appeared before Abraham. (Gen. 12:7)
וַיֵּרָ֤א אֵלָיו֙ יְהוָ֔ה
Then Yahweh appeared before him [Isaac]. (Gen. 26:24)
וַיִּקְרָ֧א יַעֲקֹ֛ב שֵׁ֥ם הַמָּקֹ֖ום פְּנִיאֵ֑ל כִּֽי־רָאִ֤יתִי אֱלֹהִים֙ פָּנִ֣ים אֶל־פָּנִ֔ים וַתִּנָּצֵ֖ל נַפְשִֽׁי
Then Jacob called the name of the place Peniel, [saying], “Because I have seen God face to face, and my soul has been delivered.” (Gen. 32:31)
וַיֹּ֤אמֶר אֱלֹהִים֙ אֶֽל־יַעֲקֹ֔ב ק֛וּם עֲלֵ֥ה בֵֽית־אֵ֖ל וְשֶׁב־שָׁ֑ם וַעֲשֵׂה־שָׁ֣ם מִזְבֵּ֔חַ לָאֵל֙ הַנִּרְאֶ֣ה אֵלֶ֔יךָ בְּבָרְחֲךָ֔ מִפְּנֵ֖י עֵשָׂ֥ו אָחִֽיךָ׃
And God said to Jacob, “Arise, and go up to byt-el, and dwell at that place. Make an alter there to El, who appeared to you when you fled from the presence of your brother Esau.” (Gen. 35:1)
וַיֵּרָ֨א אֱלֹהִ֤ים אֶֽל־יַעֲקֹב֙ עֹ֔וד בְּבֹאֹ֖ו מִפַּדַּ֣ן אֲרָ֑ם וַיְבָ֖רֶךְ אֹתֹֽו
Then God appeared before Jacob again when he came from Padan-aram, and he blessed him. (Gen. 35:9)
וַיִּרְא֕וּ אֵ֖ת אֱלֹהֵ֣י יִשְׂרָאֵ֑ל
And they saw the God of Israel. (Ex. 24:10)
וְדִבֶּ֨ר יְהוָ֤ה אֶל־מֹשֶׁה֙ פָּנִ֣ים אֶל־פָּנִ֔ים כַּאֲשֶׁ֛ר יְדַבֵּ֥ר אִ֖ישׁ אֶל־רֵעֵ֑הוּ
Yahweh would speak to Moses face to face, just as a man speaks to his companion. (Ex. 33:11)
בְּבֹ֣וא כָל־יִשְׂרָאֵ֗ל לֵרָאֹות֙ אֶת־פְּנֵי֙ יְהוָ֣ה אֱלֹהֶ֔יךָ
When all of Israel comes to appear before the face of Yahweh your God. (Deut 31:11) [Note: an alternative voweling of  לֵרָאֹות֙ would yield “to see” the face of Yahweh.]
וַיֹּ֧אמֶר מָנֹ֛וחַ אֶל־אִשְׁתֹּ֖ו מֹ֣ות נָמ֑וּת כִּ֥י אֱלֹהִ֖ים רָאִֽינוּ׃
Then Manoah said to his wife, “We will surely die, because we have seen God!” (Judges 13:22)
בַּלַּ֣יְלָה הַה֔וּא נִרְאָ֥ה אֱלֹהִ֖ים לִשְׁלֹמֹ֑ה
During the night God appeared to Solomon. (2 Chron. 1:7)
בִּשְׁנַת־מֹות֙ הַמֶּ֣לֶךְ עֻזִּיָּ֔הוּ וָאֶרְאֶ֧ה אֶת־אֲדֹנָ֛י יֹשֵׁ֥ב עַל־כִּסֵּ֖א רָ֣ם וְנִשָּׂ֑א וְשׁוּלָ֖יו מְלֵאִ֥ים אֶת־הַהֵיכָֽל׃
In the year of the death of Uzziah the king, I saw the lord sitting upon a throne, great and lifted up. The hem of his garment was willing the temple. (Isaiah 6:1)
(For now I will leave aside the implications of God being described as having a face.) 
Concerning the ability to see God in the Hebrew Bible, James Kugel remarked, “[God] was not to be represented in an image, not because He did not have a body, however, and not because He could not been seen by people. On the contrary: perhaps making an image of Him was forbidden precisely because the fact of His appearing among human beings, His being revealed, was (as we have seen) such a crucial item.” (The God of Old, 106, emphasis in original.)
Whatever the meaning of 1 Timothy 6:16, it emphatically does not mean what sectarian critics of the Church claim it means.