This is a strange take. In Japanese it’s literally a consonant cluster [ts], which is to say it’s literally a Japanese “t” followed by a Japanese “s”. The Japanese “t” and “s” are not exactly the same as English, but they’re close enough, and English has the same cluster in, say, the plural “mats” of “mat”.
What “tsunami” breaks in English is not really the sound, but instead just the fact that English doesn’t allow [ts] unless it’s preceeded by a vowel.
It’s not at all like the T sound in Japanese followed by the S sound. The normal T sound in Japanese is pronounced by putting your tongue behind your top teeth and flicking your tongue down a bit. Tsu on the other hand starts with your tongue below your top teeth, and your cheeks pulled together a bit.
It’s also nothing like the TS in Mats in english.
Where are you getting this information? This “pull your cheeks together a bit” sounds completely out of left field to me.
“Nothing like” seems to overstate things, at least to me.
Certainly, the sound in Japanese doesn’t sound aspirated the way English speakers do and expect to hear, but in listening to all the recordings at Forvo for this word, an initial “ts” seems like an entirely reasonable and fairly faithful approximation of the Japanese sound.
Granted, I would expect someone who has listened to significant amounts of Japanese to hear differences that an outsider like me wouldn’t notice, and consequently to judge differences as more pronounced than I would. Even with that in mind, “nothing like” seems like quite the exaggeration.
Moreover, and back to the original point, the pronouciation with an initial “ts” in English seems pretty obvious, just as dropping the “t” to conform to typical English phonotactics does. I wouldn’t see any reason to rule either pronunciation choice out.