The phrase "afterwards began" is correct and usable in written English.
It can be used to indicate that something started after a previous event or action.
Example: "After the meeting concluded, she afterwards began to implement the new strategies discussed."
Alternatives: "subsequently started" or "then commenced".
She published her first collection of poems in 1967 and soon afterwards began writing fiction.
I read for a degree in materials science and, afterwards, began working as a damp and timber surveyor.
His daughter received the vaccine in 2009 and in the months afterwards began showing symptoms of the sleep disorder, such as lethargy and sudden loss of muscle control.
Shortly afterwards began his lifelong career of 46 years of dedicated physician service at the Veteran's Administration Hospitals in Coatesville, Pittsburgh, and Phila, PA, Dublin, GA, and lastly in Montgomery, AL.
He returned to Cambridge and afterwards began a career in the church (though he was the exact opposite of a hell-fire preacher; I doubt if his God would have come up with the inferno).
Many of the questions afterwards began with a little mumbled, 'Liza, I've loved you all my life.' I wonder what exactly people are saying when they say that to someone they don't know; and what it feels like to hear it when it has almost become a commonplace.
Afterwards begins the happy life, where God is satisfied with you, and eternal bliss "in the company of the prophets, the companions, the martyrs and the good people, who are all good company".
The system will afterwards begin constructions of two 5 km five-station extensions, creating a two-line metro.
In the corner afterwards, Bright began talking very fast indeed.
Afterwards, Lerner began work on a long poem.
Immediately afterwards, I began receiving fake-looking Facebook friend requests.
