Not everyone loves it when the new kid shows up and starts turning heads, but sometimes there is a reason to pay attention. On the social media playground, that new kid is TikTok — and it is time for brands to take notice.

ByteDance’s addictive video app, now barely three years old, was downloaded 315 million times in the first quarter of 2020 — more than any other app has been downloaded in a single quarter, according to analytics firm Sensor Tower. Advertisers are rushing...