Who started the worship of Allah?

Answer 1

The Quran tells that the 1st thing Allah created before creating this universe (even before Adam AS) was the Noor (Light) of Muhammad and that Muhammad's Noor being the only "existing thing", worshiped Allah.

Then Allah created skies, paradise, angels, houris, hell, planets, spirits of all the human beings, stars etc and all of them had their own way of worshiping Allah.

Among humans worshiping Allah started with the creation of Adam (AS) and Hawwa (Eve AS) who worshiped Him in Paradise according to the way inspired in their hearts by Allah.

There are many ways to worship Allah from rembering him in heart, in open, doing good deeds to others, acquiring and spreading knowledge of religion as well as world knowledge to benefit others, praying, struggling in his cause with your wealth and even with your life if the need arises and even removing a stone or throne form someone's path is worshiping Allah.

If you're asking about the current "Prayer" way of worshiping Allah, it was told to Muslims by Muhammad (Peace Be Upon Him) but had been in effect since Adam and Eve (AS) with some very minor differences.

Answer 2

Since start of universe creation and Adam creation. Refer to question below.