The English word 'pun' is equivalent to the Hebrew 'al tiqre . . . ellaʾ (“do not read . . . but”) which allows the interpreter to exchange one vowel or consonant for another.
The 22 letters of the Hebrew alphabet divide into 5 phonetic groups, based on their origin in the mouth's vocal system:
the throat: א (alef) ח (chet) ה (hei) ע (ayin)
the palate: ג (gimel) י (yud) כ (kaf) ק (kuf)
the tongue: ז (zayin) ש (shin) ס (samech) ר (raish) צ (tzadik)
the teeth: ד (dalet) ט (tet) ל (lamed) נ (noon) ת (tav)
the lips: ב (bet) ו (vav) מ (mem) פ (pai)
Phonetically, any two letters of the same origin can be interchanged. Thus, there are many Hebrew words whose proximity in meaning derives from their phonetic equivalence. Words made in this way which do not have similar meanings can replace one another as 'puns'.
There is another kind of pun where words with different meanings differ only by vowels added later. These puns were manufactured by the addition of vowels. In reality the original word contained the differing meanings. These are identified by dropping the late addition vowels. I use 'late addition vowels' because four of the original Hebrew letters actually act like vowels and are recognized as such by some sages.
Then in Kabbalah every letter and every combination of letters is analyzed and understood in its own right.
The word bereisheet has three root letters (ROSh), a one letter prefix (B) and a two-letter suffix (eeT). But there are three two-letter sub root combinations as well. The two-letter sub-roots are a core idea which tie together three-letter roots formed by adding one of the four vowel letters. The roots are all aspects of the same core idea. Though they are not considered Hebrew puns technically, effectively the two-letter sub-roots can be considered embedded puns.
There are other word-play devices involving numerations and single-letter meanings, but these would be an even greater stretch to call them puns.
The plausibility of a pun depends on the interpretive structure. In literal methods most puns are viewed as accidental and incidental to the interpretation since only a single literal meaning is being sought. In Jewish Kabbalah they all have meaning, and though we may not currently understand them, we are to wrestle until we find answers. In sensus plenior, the rules filter out the implausible, since only solutions which point to Christ are sought.
For non-Hebrew speakers:
As you are using your Hebrew dictionary, browse before and after the word you are looking at to see other words that share the same consonants. This will identify 'manufactured puns'. Use the letter substitutions above and look up the new words formed to see if the word is productive within your interpretive framework. These are the proper puns. You must be able to identify letters do do this as well as to identify two-letter embedded puns.
If you can pronounce the word, then any other word or combination of words that sounds like it is a candidate for being a pun. Ultimately it is child's play.
Two-letter Subroots and Individual Letters
The word bereisheet has three root letters () and three additional
letters: a oneletter prefix () and a two-letter suffix (). The
three root letters spell the word rosh, meaning "head" or "beginning."
However, in Kabbalah every letter and every combination of letters
is analyzed and understood in its own right. The first two letter
unit that begins the whole Torah and the whole creative process is
therefore BR. The second two letters are ShA , which means fire and the
two suffix letters (YTh) are also considered as a third unit on their
Harav Yitzchak Ginsburgh p.9