This grammatical analysis comes from Victor Hamilton.

The word is בְּרֵאשִׁית (ber’eshith): a preposition "in" with "beginning; starting point." You're correct that it's anarthrous (no article). There are four possibilities of translation, then:

1. In an absolute sense as an independent clause: In the beginning. This option teaches an absolute beginning of creation as a direct act of God.
2. An indeterminate noun, used as a relative temporal designation: Initially God created…
3. Construct state, temporal clause subordinate to v. 2: When God began to create. …. This option affirms the existence of matter before the creation of heaven and earth.
4. Construct state, temporal clause subordinate to v. 3: When God began to create… This option affirms the existence of matter before the creation of heaven and earth.

Choices 1 and 4 have the widest support, with Choice 1 having the best substantiation.

In Genesis 1:1 in the original Hebrew there is no definite article before the word beginning. So how come the verse is translated as “In THE beginning ...” instead of “In A beginning ...”?