Up here, someone can be cremated immediately, ashes kept by family member until a memorial service of some kind......several weeks/months later. Depending on ability of all family to arrange to get away at same time. When my cousin passed away, in Illinois, NO funeral or service, but the at home daughter sent some ashes to both sisters who lived in Calif. and in Tenn.
However, when my mother-in-law passed away, (Illinois) yes, brother-in-law arranged that her service was nearly immediate, within next day or two, and it was very difficult for us to get away, business/children, with such short notice. She passed on Thurs., funeral was Sat. And the other brothers also lived out of state. Same for them.