Tarawih prayer is a confirmed Sunnah that the Prophet (peace and blessings be upon him) performed. Thus, Tarawih was not started by `Umar (may Allah be pleased with him). Rather, it was started by the Prophet himself, but he didn’t continue to pray it in congregation so that zealous Muslims wouldn’t think that it was obligatory on them.
Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states the following: It is not at all true to say that Tarawih Prayer was started by `Umar (may Allah be pleased with him). It was started by the Prophet (peace and blessings be upon him), but he didn’t continue praying it in congregation, as he was afraid of Allah making it obligatory on the faithful because of the great zeal they showed, as they had come out in overwhelming numbers to the Mosque. So, the Prophet (peace and blessings be upon him) left it as a Sunnah.
`Umar ibn Al-Khattab (may Allah be pleased with him) and other companions knew this point well, and so they did not do anything other than calling people back to the Mosque, especially when they knew that there was no fear now of Allah declaring Tarawih as obligatory because the revelation had stopped with the death of the Prophet (peace and blessings be upon him).
The Muslim community has rightly followed the footsteps of the Prophet and the righteous caliphs in maintaining this institution as the Prophet (peace and blessings be upon him) wanted it.