Adam the Muslim?

Muslims opine that Islam goes back to Adam.

Ibn 'Umar (May Allah be pleased with them) reported:

The Messenger of Allah (ﷺ) said, "(The structure of) Islam is built on five (pillars): Testification of 'La ilaha illallah' (none has the right to be worshipped but Allah), that Muhammad (ﷺ) is his slave and Messenger, the establishment of Salat, the payment of Zakat, the pilgrimage to the House of Allah (Ka'bah), and Saum during the month of Ramadan."

[Al-Bukhari and Muslim].

https://sunnah.com/riyadussalihin:1206

As Islam was BUILT, it must have had a beginning. We might suppose, were Islam true, that the angels are Muslims. See: Is Everyone and Everything Muslim? Might they be saying Shahadah, doing salat, as opposed to simply praying, paying zakat, doing Hajj and fasting? Had Adam been a Muslim, might he have been doing all this? Might Adam, who, being a prophet, was a messenger, have been saying that the founder of Islam was Allah's messenger? He didn't live until the 7th century. The Arabic for "Saum during the month of Ramadan" is صوم رمضان, sawm Ramadan, Ramadan fast. As this fast was something of an afterthought, how might Adam have been observing it? Before this fast, Muslims were observing the Ashura fast. See: Ashura