Please inform me at once if you have got any news.(如果有新消息请第一时间告诉我)
Please inform me at once if there is any progress.(如果有新进展请第一时间告诉我)
Please tell me in the first time.
PLEASE tell me at once.
直接一点的话,用At the first second, 就比较接近 直译 第一时间了,否则的话 用at first time. 比较容易和 第一次混淆。