The phrase "big breakout" refers to a significant or major event or achievement that propels someone or something to sudden success or popularity. Full definition
Her performance was so great that I'm still waiting for her to become the next big breakout star. (pastemagazine.com)
I was skeptical that 2017 would be virtual reality's big breakout year, having been burned on the technology before, but I tried to keep an open mind. (tomsguide.com)
Otherwise, this is one of TIFF's big breakout hits, and one you'll be hearing a lot about as the awards season heats up. (joblo.com)