Is Ghusl permissible without an order of washing?

For its bare obligations, can I rub my entire body with water, rinse my mouth and nose, without order and will the ghusl still be valid?

as-salamu alaikum,

akhil kareem, this are the obligatory acts of ghusl:

١ - النية لرفع الحدث الأكبر مقارنة.

٢ - والمضمضة والاستنشاق.

٣ - وعم البدن بإجراء الماء والدلك.

٤ - وعلى الرجل نقض الشعر، وعلى المرأة في الدمين: دم الحيض، والنفاس.

Intention to remove the major state of ritual impurity, made simultaneously with the act.

Rinsing the mouth and inhaling water into the nose (and blowing it out).

Washing the entire body, ensuring water reaches all parts, along with rubbing (the body).

For a man, undoing the hair is required;
for a woman, it is required only in the two cases of menstrual bleeding and postpartum bleeding.

Quote from al-Mukhtasar al-Mufid


So the order is not one of its obligations.
wa salam