Minchat Shai, Bereishit 1:1

Here is Bereishit 1:1:

בְּרֵאשִׁ֖ית בָּרָ֣א אֱלֹהִ֑ים אֵ֥ת הַשָּׁמַ֖יִם וְאֵ֥ת הָאָֽרֶץ׃

Minchat Shai comments:

בְּרֵאשִׁית דגש הבי"ת עם טפחא תחת השי"ן. ב' רבתי. ובראש השיטה ובראש הדף וזו היא בי"ת של בי"ה שמ"ו. עיין ברבינו בחיי פ' בשלח וריקנאטי ריש פ' בראשית ובפי' שערי אורה למהר"ר מתתיה דלאקרט ז"ל במדה ראשונה על מלת ואת:

To analyze this, piece by piece.

דגש הבי"ת עם טפחא תחת השי"ן

The bet gets a dagesh. This is obvious and unsurprising, as a straightforward application of the rule that beged kefet at the start of a word will take a dagesh kal, indicating that it is the plosive rather than fricative. So, it is a bet rather than bhet.

עם טפחא תחת השי"ן.

Is this obvious, or are there contrary texts? I'll point to William Wickes (in A Treatise on the accentuation of the twenty-one so-called Prose books of the Old Testament), page 32, who asserts that the rules of trup, if only looking to the logical (followed by syntactic division) would have been other than what we have, but the etnachta is placed on Elokim for emphasis. Otherwise, presumably, the logical division would be on Bereishit. 

Once the etnachta is on Elokim, the syntactic division would separate of the PP (prepositional phrase) from the VP (verb phrase), and one or two words away from the etnachta, we can have a tipcha as the disjunctive accent. This all follows from a modern analysis of trup, which isn't necessarily what would motivate Minchat Shai. More likely, it is simply that this is the very first word of Tanach, so gets focus.

 ב' רבתי. ובראש השיטה ובראש הדף וזו היא בי"ת של בי"ה שמ"ו

An enlarged bet. And this is at the start of a line, at the start of a column. And this is the bet of the mnemonic of  בי"ה שמ"ו, (a quote of Tehillim 68:5) which are letters that start columns. These are:

YUD - Bereshit 49:8

HEH - Shemot 14:28

SHIN - dispute. See Minchat Shai to Vayikra 18:8

MEM - dispute. See Minchat Shai to Bemidbar 24:5

VAV - Devarim 31:28.

 עיין ברבינו בחיי פ' בשלח

This is to explain the masoretic note. Rabbenu Bachya on Shemot 14:28 begins:

הבאים אחריהם בים. משפט ס"ת להיות ששה בריש דפין והסימן הוא בי"ה שמ"ו. ואלו הם, ב'ראשית, י'הודה אתה יודוך, ה'באים אחריהם, ש'מור ושמעת, מ'צא שפתיך, ו'אעידה בם,

and Rabbenu Bachya proceeds to offer a reason. The SHIN would be Devarim 12:28, the MEM would be Devarim 23:24, and the YUD would be Devarim 31:28.

וריקנאטי ריש פ' בראשית

Recanati at the start of Bereshit discusses, from a kabbalistic perspective, why the Torah begins with the letter bet.

ובפי' שערי אורה למהר"ר מתתיה דלאקרט ז"ל במדה ראשונה על מלת ואת

And in Shaarei Ora, from Rabbi Matitya Delecrut (with R' Yosef Gikatillia), in the midda rishona, on the word ve'et.  (Another kabbalistic work. unsure what it says there.)