How Do You Pronounce “Suggest”?

I was reading about words in English with a double soft G (“suggest,” “exaggerate,” and “Reggie”) and apparently the “American” pronunciation of “suggest” is something like “sug-JEST” with a hard G sound in the middle, which is blowing my mind right now.

Merriam-Webster even lists it first before “su-JEST” which is supposedly the “British” pronunciation as well as how I pronounce it.