Is there English counterpart to Japanese proverb, 一期一会 , meaning "Cherish once -in -a-lifetime encounter"?

In the far more general sense, there is carpe diem ("seize the day"), "you only go around once" (or "I shall pass through this world but once"), "make hay while the sun shines", and of course, "YOLO".

You cannot step twice into the same river is in proverbial use in Czech, and I've thought of it as such, but in fact it appears to be a quote from Heraclitus.

The observation would be that seemingly ordinary, everyday events of life are in fact unique.

Oishi-san, as a former advertising professional you might enjoy knowing that the saying that possibly comes closest to this is possibly an old ad slogan, apparently from the mid-'60s:

You never get a second chance to make a first impression.

See this thread and a search for the expression leads to many others.

Advertising, of course, is well known for borrowing ideas, so this may not be original with the copywriter who penned it. But I think the saying fits.

I think the idiom once-in-a-lifetime chance/opportunity conveys the idea in a broad sense.

Ichi-go ichi-e (一期一会) is a cultural concept in Japan and it is more associated with meeting people. It is also translated as "Treasure every encounter, for it will never recur."